Definitions for contractions (varipeps.contractions.Definitions)

class varipeps.contractions.Definitions

Bases: object

Class to define the contractions used along in this package.

The convention used for the ordering of the tensors is for a single PEPS tensor:

single = [PEPS tensor, relevant CTM tensors starting at C1 and then clockwise]

which is repeated for each PEPS tensor and its environment in the ordering fixed x and all corresponding y values in increasing order and then the next x value in increasing order. For example for a quadratic four site the structure would look like:

 (x, y)  -  (x, y+1)
   |           |
(x+1, y) - (x+1, y+1)

tensors = [single(x, y), single(x, y+1), single(x+1, y), single(x+1, y+1)]

Using this convention each contraction is specified in the format:

contraction_name = {
  "tensors": [
    [Relevant elements for first single PEPS tensors incl. env],
    [Relevant elements for second single PEPS tensors incl. env],
    ...,
    "Optional string elements indicating additional non-PEPS tensors (e.g. gates)"
  ],
  "network": [
    [
      (Axes for first element of the tensors for first PEPS Tensor),
      (Axes for second element of the tensors for first PEPS Tensor)
    ],
    [
      (Axes for first element of the tensors for second PEPS Tensor),
      (Axes for second element of the tensors for second PEPS Tensor)
    ],
    ...,
    (Axes for additional non-PEPS tensors)
  ]
}

The axes are hereby specified in the ncon format where positive numbers describes the axes to be contracted and negative number the open axes after the contraction. The elements are strings indicating the elements of the PEPS tensor object elements. Hereby the special element “tensor_conj” describes the conjugated and transposed PEPS tensor.

classmethod add_def(name, definition)

corrlength_absorb_one_column: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dicYe,fjcXg,begZ,hWji,bdfh->ZYXW', 'filter_additional_tensors': ['vec'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'T3']], 'ncon_network': [(3, 8, 2, -2, 4), (5, 9, 2, -3, 6), (1, 4, 6, -1), (7, -4, 9, 8), [1, 3, 5, 7]], 'network': [[(3, 8, 2, -2, 4), (5, 9, 2, -3, 6), (1, 4, 6, -1), (7, -4, 9, 8)], [1, 3, 5, 7]], 'network_additional_tensors': [[1, 3, 5, 7]], 'network_peps_tensors': [[(3, 8, 2, -2, 4), (5, 9, 2, -3, 6), (1, 4, 6, -1), (7, -4, 9, 8)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'T3'], 'vec']}

corrlength_absorb_one_row: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eYcid,gXcjf,Zgeb,ijWh,bdfh->ZYXW', 'filter_additional_tensors': ['vec'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4', 'T2']], 'ncon_network': [(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (-1, 6, 4, 1), (8, 9, -4, 7), [1, 3, 5, 7]], 'network': [[(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (-1, 6, 4, 1), (8, 9, -4, 7)], [1, 3, 5, 7]], 'network_additional_tensors': [[1, 3, 5, 7]], 'network_peps_tensors': [[(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (-1, 6, 4, 1), (8, 9, -4, 7)]], 'tensors': [['tensor', 'tensor_conj', 'T4', 'T2'], 'vec']}

corrlength_transfer_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cUbeY,dTbfX,VdcZ,efSW->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4', 'T2']], 'ncon_network': [(2, -6, 1, 4, -2), (3, -7, 1, 5, -3), (-5, 3, 2, -1), (4, 5, -8, -4)], 'network': [[(2, -6, 1, 4, -2), (3, -7, 1, 5, -3), (-5, 3, 2, -1), (4, 5, -8, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(2, -6, 1, 4, -2), (3, -7, 1, 5, -3), (-5, 3, 2, -1), (4, 5, -8, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T4', 'T2']]}

corrlength_transfer_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YebUc,XfbTd,ZcdV,WSfe->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'T3']], 'ncon_network': [(-2, 4, 1, -6, 2), (-3, 5, 1, -7, 3), (-1, 2, 3, -5), (-4, -8, 5, 4)], 'network': [[(-2, 4, 1, -6, 2), (-3, 5, 1, -7, 3), (-1, 2, 3, -5), (-4, -8, 5, 4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 4, 1, -6, 2), (-3, 5, 1, -7, 3), (-1, 2, 3, -5), (-4, -8, 5, 4)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'T3']]}

corrlength_vector_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bZ,bcXY,cW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C4', 'T3', 'C3']], 'ncon_network': [(1, -1), (1, 2, -3, -2), (2, -4)], 'network': [[(1, -1), (1, 2, -3, -2), (2, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(1, -1), (1, 2, -3, -2), (2, -4)]], 'tensors': [['C4', 'T3', 'C3']]}

corrlength_vector_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bZ,cXYb,Wc->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C1', 'T4', 'C4']], 'ncon_network': [(1, -1), (2, -3, -2, 1), (-4, 2)], 'network': [[(1, -1), (2, -3, -2, 1), (-4, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(1, -1), (2, -3, -2, 1), (-4, 2)]], 'tensors': [['C1', 'T4', 'C4']]}

corrlength_vector_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zb,YXcb,Wc->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C2', 'T2', 'C3']], 'ncon_network': [(-1, 1), (-2, -3, 2, 1), (-4, 2)], 'network': [[(-1, 1), (-2, -3, 2, 1), (-4, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-1, 1), (-2, -3, 2, 1), (-4, 2)]], 'tensors': [['C2', 'T2', 'C3']]}

corrlength_vector_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zb,bYXc,cW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C1', 'T1', 'C2']], 'ncon_network': [(-1, 1), (1, -2, -3, 2), (2, -4)], 'network': [[(-1, 1), (1, -2, -3, 2), (2, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-1, 1), (1, -2, -3, 2), (2, -4)]], 'tensors': [['C1', 'T1', 'C2']]}

ctmrg_absorption_bottom_C3: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'debY,cb,cedZ->ZY', 'filter_additional_tensors': ['projector_bottom_left'], 'filter_peps_tensors': [['T2', 'C3']], 'ncon_network': [(3, 4, 1, -2), (2, 1), (2, 4, 3, -1)], 'network': [[(3, 4, 1, -2), (2, 1)], (2, 4, 3, -1)], 'network_additional_tensors': [(2, 4, 3, -1)], 'network_peps_tensors': [[(3, 4, 1, -2), (2, 1)]], 'tensors': [['T2', 'C3'], 'projector_bottom_left']}

Fig. 4 Contraction for C3 during bottom absorption.

ctmrg_absorption_bottom_C3_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'debY,cb,cedZ->ZY', 'filter_additional_tensors': ['projector_bottom_left'], 'filter_peps_tensors': [['T2', 'C3_phase']], 'ncon_network': [(3, 4, 1, -2), (2, 1), (2, 4, 3, -1)], 'network': [[(3, 4, 1, -2), (2, 1)], (2, 4, 3, -1)], 'network_additional_tensors': [(2, 4, 3, -1)], 'network_peps_tensors': [[(3, 4, 1, -2), (2, 1)]], 'tensors': [['T2', 'C3_phase'], 'projector_bottom_left']}

Fig. 5 Contraction for C3 during bottom absorption. Here C3 is the tensor with structure factor phase included which is grown by a normal T2 tensor.

ctmrg_absorption_bottom_C3_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'debY,cb,cedZ->ZY', 'filter_additional_tensors': ['projector_bottom_left'], 'filter_peps_tensors': [['T2_phase', 'C3']], 'ncon_network': [(3, 4, 1, -2), (2, 1), (2, 4, 3, -1)], 'network': [[(3, 4, 1, -2), (2, 1)], (2, 4, 3, -1)], 'network_additional_tensors': [(2, 4, 3, -1)], 'network_peps_tensors': [[(3, 4, 1, -2), (2, 1)]], 'tensors': [['T2_phase', 'C3'], 'projector_bottom_left']}

Fig. 6 Contraction for C3 during bottom absorption. Here C3 is the tensor with structure factor phase not included yet which is grown by a T2 tensor which includes a phase already.

ctmrg_absorption_bottom_C4: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,bedY,Zced->ZY', 'filter_additional_tensors': ['projector_bottom_right'], 'filter_peps_tensors': [['C4', 'T4']], 'ncon_network': [(2, 1), (1, 4, 3, -2), (-1, 2, 4, 3)], 'network': [[(2, 1), (1, 4, 3, -2)], (-1, 2, 4, 3)], 'network_additional_tensors': [(-1, 2, 4, 3)], 'network_peps_tensors': [[(2, 1), (1, 4, 3, -2)]], 'tensors': [['C4', 'T4'], 'projector_bottom_right']}

Fig. 7 Contraction for C4 during bottom absorption.

ctmrg_absorption_bottom_C4_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,bedY,Zced->ZY', 'filter_additional_tensors': ['projector_bottom_right'], 'filter_peps_tensors': [['C4_phase', 'T4']], 'ncon_network': [(2, 1), (1, 4, 3, -2), (-1, 2, 4, 3)], 'network': [[(2, 1), (1, 4, 3, -2)], (-1, 2, 4, 3)], 'network_additional_tensors': [(-1, 2, 4, 3)], 'network_peps_tensors': [[(2, 1), (1, 4, 3, -2)]], 'tensors': [['C4_phase', 'T4'], 'projector_bottom_right']}

Fig. 8 Contraction for C4 during bottom absorption. Here C4 is the tensor with structure factor phase included which is grown by a normal T4 tensor.

ctmrg_absorption_bottom_C4_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,bedY,Zced->ZY', 'filter_additional_tensors': ['projector_bottom_right'], 'filter_peps_tensors': [['C4', 'T4_phase']], 'ncon_network': [(2, 1), (1, 4, 3, -2), (-1, 2, 4, 3)], 'network': [[(2, 1), (1, 4, 3, -2)], (-1, 2, 4, 3)], 'network_additional_tensors': [(-1, 2, 4, 3)], 'network_peps_tensors': [[(2, 1), (1, 4, 3, -2)]], 'tensors': [['C4', 'T4_phase'], 'projector_bottom_right']}

Fig. 9 Contraction for C4 during bottom absorption. Here C4 is the tensor with structure factor phase not included yet which is grown by a T4 tensor which includes a phase already.

ctmrg_absorption_bottom_T3: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dcgiW,fegjX,bhec,bfdZ,Yhji->ZYXW', 'filter_additional_tensors': ['projector_bottom_left', 'projector_bottom_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3']], 'ncon_network': [(3, 2, 6, 8, -4), (5, 4, 6, 9, -3), (1, 7, 4, 2), (1, 5, 3, -1), (-2, 7, 9, 8)], 'network': [[(3, 2, 6, 8, -4), (5, 4, 6, 9, -3), (1, 7, 4, 2)], (1, 5, 3, -1), (-2, 7, 9, 8)], 'network_additional_tensors': [(1, 5, 3, -1), (-2, 7, 9, 8)], 'network_peps_tensors': [[(3, 2, 6, 8, -4), (5, 4, 6, 9, -3), (1, 7, 4, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T3'], 'projector_bottom_left', 'projector_bottom_right']}

Fig. 10 Contraction for T3 during bottom absorption.

ctmrg_absorption_bottom_T3_large_d: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'edciW,gfcjX,bhfd,bgeZ,Yhji->ZYXW', 'filter_additional_tensors': ['projector_bottom_left', 'projector_bottom_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3']], 'ncon_network': [(4, 3, 2, 8, -4), (6, 5, 2, 9, -3), (1, 7, 5, 3), (1, 6, 4, -1), (-2, 7, 9, 8)], 'network': [[(4, 3, 2, 8, -4), (6, 5, 2, 9, -3), (1, 7, 5, 3)], (1, 6, 4, -1), (-2, 7, 9, 8)], 'network_additional_tensors': [(1, 6, 4, -1), (-2, 7, 9, 8)], 'network_peps_tensors': [[(4, 3, 2, 8, -4), (6, 5, 2, 9, -3), (1, 7, 5, 3)]], 'tensors': [['tensor', 'tensor_conj', 'T3'], 'projector_bottom_left', 'projector_bottom_right']}

ctmrg_absorption_bottom_T3_large_d_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'edciW,gfcjX,bhfd,bgeZ,Yhji->ZYXW', 'filter_additional_tensors': ['projector_bottom_left', 'projector_bottom_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3_phase']], 'ncon_network': [(4, 3, 2, 8, -4), (6, 5, 2, 9, -3), (1, 7, 5, 3), (1, 6, 4, -1), (-2, 7, 9, 8)], 'network': [[(4, 3, 2, 8, -4), (6, 5, 2, 9, -3), (1, 7, 5, 3)], (1, 6, 4, -1), (-2, 7, 9, 8)], 'network_additional_tensors': [(1, 6, 4, -1), (-2, 7, 9, 8)], 'network_peps_tensors': [[(4, 3, 2, 8, -4), (6, 5, 2, 9, -3), (1, 7, 5, 3)]], 'tensors': [['tensor', 'tensor_conj', 'T3_phase'], 'projector_bottom_left', 'projector_bottom_right']}

ctmrg_absorption_bottom_T3_large_d_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fecjW,hgdkX,bige,bhfZ,Yikj,cd->ZYXW', 'filter_additional_tensors': ['projector_bottom_left', 'projector_bottom_right', 'structure_factor_gate'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3']], 'ncon_network': [(5, 4, 2, 9, -4), (7, 6, 3, 10, -3), (1, 8, 6, 4), (1, 7, 5, -1), (-2, 8, 10, 9), (2, 3)], 'network': [[(5, 4, 2, 9, -4), (7, 6, 3, 10, -3), (1, 8, 6, 4)], (1, 7, 5, -1), (-2, 8, 10, 9), (2, 3)], 'network_additional_tensors': [(1, 7, 5, -1), (-2, 8, 10, 9), (2, 3)], 'network_peps_tensors': [[(5, 4, 2, 9, -4), (7, 6, 3, 10, -3), (1, 8, 6, 4)]], 'tensors': [['tensor', 'tensor_conj', 'T3'], 'projector_bottom_left', 'projector_bottom_right', 'structure_factor_gate']}

ctmrg_absorption_left_C1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,bdeY,Zcde->ZY', 'filter_additional_tensors': ['projector_left_bottom'], 'filter_peps_tensors': [['C1', 'T1']], 'ncon_network': [(2, 1), (1, 3, 4, -2), (-1, 2, 3, 4)], 'network': [[(2, 1), (1, 3, 4, -2)], (-1, 2, 3, 4)], 'network_additional_tensors': [(-1, 2, 3, 4)], 'network_peps_tensors': [[(2, 1), (1, 3, 4, -2)]], 'tensors': [['C1', 'T1'], 'projector_left_bottom']}

Fig. 11 Contraction for C1 during left absorption.

ctmrg_absorption_left_C1_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,bdeY,Zcde->ZY', 'filter_additional_tensors': ['projector_left_bottom'], 'filter_peps_tensors': [['C1_phase', 'T1']], 'ncon_network': [(2, 1), (1, 3, 4, -2), (-1, 2, 3, 4)], 'network': [[(2, 1), (1, 3, 4, -2)], (-1, 2, 3, 4)], 'network_additional_tensors': [(-1, 2, 3, 4)], 'network_peps_tensors': [[(2, 1), (1, 3, 4, -2)]], 'tensors': [['C1_phase', 'T1'], 'projector_left_bottom']}

Fig. 12 Contraction for C1 during left absorption. Here C1 is the tensor with structure factor phase included which is grown by a normal T1 tensor.

ctmrg_absorption_left_C1_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,bdeY,Zcde->ZY', 'filter_additional_tensors': ['projector_left_bottom'], 'filter_peps_tensors': [['C1', 'T1_phase']], 'ncon_network': [(2, 1), (1, 3, 4, -2), (-1, 2, 3, 4)], 'network': [[(2, 1), (1, 3, 4, -2)], (-1, 2, 3, 4)], 'network_additional_tensors': [(-1, 2, 3, 4)], 'network_peps_tensors': [[(2, 1), (1, 3, 4, -2)]], 'tensors': [['C1', 'T1_phase'], 'projector_left_bottom']}

Fig. 13 Contraction for C1 during left absorption. Here C1 is the tensor with structure factor phase not included yet which is grown by a T1 tensor which includes a phase already.

ctmrg_absorption_left_C4: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bZed,bc,cdeY->ZY', 'filter_additional_tensors': ['projector_left_top'], 'filter_peps_tensors': [['T3', 'C4']], 'ncon_network': [(1, -1, 4, 3), (1, 2), (2, 3, 4, -2)], 'network': [[(1, -1, 4, 3), (1, 2)], (2, 3, 4, -2)], 'network_additional_tensors': [(2, 3, 4, -2)], 'network_peps_tensors': [[(1, -1, 4, 3), (1, 2)]], 'tensors': [['T3', 'C4'], 'projector_left_top']}

Fig. 14 Contraction for C4 during left absorption.

ctmrg_absorption_left_C4_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bZed,bc,cdeY->ZY', 'filter_additional_tensors': ['projector_left_top'], 'filter_peps_tensors': [['T3', 'C4_phase']], 'ncon_network': [(1, -1, 4, 3), (1, 2), (2, 3, 4, -2)], 'network': [[(1, -1, 4, 3), (1, 2)], (2, 3, 4, -2)], 'network_additional_tensors': [(2, 3, 4, -2)], 'network_peps_tensors': [[(1, -1, 4, 3), (1, 2)]], 'tensors': [['T3', 'C4_phase'], 'projector_left_top']}

Fig. 15 Contraction for C4 during left absorption. Here C4 is the tensor with structure factor phase included which is grown by a normal T3 tensor.

ctmrg_absorption_left_C4_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bZed,bc,cdeY->ZY', 'filter_additional_tensors': ['projector_left_top'], 'filter_peps_tensors': [['T3_phase', 'C4']], 'ncon_network': [(1, -1, 4, 3), (1, 2), (2, 3, 4, -2)], 'network': [[(1, -1, 4, 3), (1, 2)], (2, 3, 4, -2)], 'network_additional_tensors': [(2, 3, 4, -2)], 'network_peps_tensors': [[(1, -1, 4, 3), (1, 2)]], 'tensors': [['T3_phase', 'C4'], 'projector_left_top']}

Fig. 16 Contraction for C4 during left absorption. Here C3 is the tensor with structure factor phase not included yet which is grown by a T3 tensor which includes a phase already.

ctmrg_absorption_left_T4: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'digXc,ejgYf,hedb,bcfW,Zhij->ZYXW', 'filter_additional_tensors': ['projector_left_top', 'projector_left_bottom'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4']], 'ncon_network': [(3, 8, 6, -3, 2), (4, 9, 6, -2, 5), (7, 4, 3, 1), (1, 2, 5, -4), (-1, 7, 8, 9)], 'network': [[(3, 8, 6, -3, 2), (4, 9, 6, -2, 5), (7, 4, 3, 1)], (1, 2, 5, -4), (-1, 7, 8, 9)], 'network_additional_tensors': [(1, 2, 5, -4), (-1, 7, 8, 9)], 'network_peps_tensors': [[(3, 8, 6, -3, 2), (4, 9, 6, -2, 5), (7, 4, 3, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T4'], 'projector_left_top', 'projector_left_bottom']}

Fig. 17 Contraction for T4 during left absorption.

ctmrg_absorption_left_T4_large_d: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eicXd,fjcYg,hfeb,bdgW,Zhij->ZYXW', 'filter_additional_tensors': ['projector_left_top', 'projector_left_bottom'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4']], 'ncon_network': [(4, 8, 2, -3, 3), (5, 9, 2, -2, 6), (7, 5, 4, 1), (1, 3, 6, -4), (-1, 7, 8, 9)], 'network': [[(4, 8, 2, -3, 3), (5, 9, 2, -2, 6), (7, 5, 4, 1)], (1, 3, 6, -4), (-1, 7, 8, 9)], 'network_additional_tensors': [(1, 3, 6, -4), (-1, 7, 8, 9)], 'network_peps_tensors': [[(4, 8, 2, -3, 3), (5, 9, 2, -2, 6), (7, 5, 4, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T4'], 'projector_left_top', 'projector_left_bottom']}

ctmrg_absorption_left_T4_large_d_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eicXd,fjcYg,hfeb,bdgW,Zhij->ZYXW', 'filter_additional_tensors': ['projector_left_top', 'projector_left_bottom'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4_phase']], 'ncon_network': [(4, 8, 2, -3, 3), (5, 9, 2, -2, 6), (7, 5, 4, 1), (1, 3, 6, -4), (-1, 7, 8, 9)], 'network': [[(4, 8, 2, -3, 3), (5, 9, 2, -2, 6), (7, 5, 4, 1)], (1, 3, 6, -4), (-1, 7, 8, 9)], 'network_additional_tensors': [(1, 3, 6, -4), (-1, 7, 8, 9)], 'network_peps_tensors': [[(4, 8, 2, -3, 3), (5, 9, 2, -2, 6), (7, 5, 4, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T4_phase'], 'projector_left_top', 'projector_left_bottom']}

ctmrg_absorption_left_T4_large_d_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fjcXe,gkdYh,igfb,behW,Zijk,cd->ZYXW', 'filter_additional_tensors': ['projector_left_top', 'projector_left_bottom', 'structure_factor_gate'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4']], 'ncon_network': [(5, 9, 2, -3, 4), (6, 10, 3, -2, 7), (8, 6, 5, 1), (1, 4, 7, -4), (-1, 8, 9, 10), (2, 3)], 'network': [[(5, 9, 2, -3, 4), (6, 10, 3, -2, 7), (8, 6, 5, 1)], (1, 4, 7, -4), (-1, 8, 9, 10), (2, 3)], 'network_additional_tensors': [(1, 4, 7, -4), (-1, 8, 9, 10), (2, 3)], 'network_peps_tensors': [[(5, 9, 2, -3, 4), (6, 10, 3, -2, 7), (8, 6, 5, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T4'], 'projector_left_top', 'projector_left_bottom', 'structure_factor_gate']}

ctmrg_absorption_right_C2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zdeb,bc,cedY->ZY', 'filter_additional_tensors': ['projector_right_bottom'], 'filter_peps_tensors': [['T1', 'C2']], 'ncon_network': [(-1, 3, 4, 1), (1, 2), (2, 4, 3, -2)], 'network': [[(-1, 3, 4, 1), (1, 2)], (2, 4, 3, -2)], 'network_additional_tensors': [(2, 4, 3, -2)], 'network_peps_tensors': [[(-1, 3, 4, 1), (1, 2)]], 'tensors': [['T1', 'C2'], 'projector_right_bottom']}

Fig. 18 Contraction for C2 during right absorption.

ctmrg_absorption_right_C2_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zdeb,bc,cedY->ZY', 'filter_additional_tensors': ['projector_right_bottom'], 'filter_peps_tensors': [['T1', 'C2_phase']], 'ncon_network': [(-1, 3, 4, 1), (1, 2), (2, 4, 3, -2)], 'network': [[(-1, 3, 4, 1), (1, 2)], (2, 4, 3, -2)], 'network_additional_tensors': [(2, 4, 3, -2)], 'network_peps_tensors': [[(-1, 3, 4, 1), (1, 2)]], 'tensors': [['T1', 'C2_phase'], 'projector_right_bottom']}

Fig. 19 Contraction for C2 during right absorption. Here C2 is the tensor with structure factor phase included which is grown by a normal T1 tensor.

ctmrg_absorption_right_C2_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zdeb,bc,cedY->ZY', 'filter_additional_tensors': ['projector_right_bottom'], 'filter_peps_tensors': [['T1_phase', 'C2']], 'ncon_network': [(-1, 3, 4, 1), (1, 2), (2, 4, 3, -2)], 'network': [[(-1, 3, 4, 1), (1, 2)], (2, 4, 3, -2)], 'network_additional_tensors': [(2, 4, 3, -2)], 'network_peps_tensors': [[(-1, 3, 4, 1), (1, 2)]], 'tensors': [['T1_phase', 'C2'], 'projector_right_bottom']}

Fig. 20 Contraction for C2 during right absorption. Here C2 is the tensor with structure factor phase not included yet which is grown by a T1 tensor which includes a phase already.

ctmrg_absorption_right_C3: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,Zbed,Yced->ZY', 'filter_additional_tensors': ['projector_right_top'], 'filter_peps_tensors': [['C3', 'T3']], 'ncon_network': [(1, 2), (-1, 1, 4, 3), (-2, 2, 4, 3)], 'network': [[(1, 2), (-1, 1, 4, 3)], (-2, 2, 4, 3)], 'network_additional_tensors': [(-2, 2, 4, 3)], 'network_peps_tensors': [[(1, 2), (-1, 1, 4, 3)]], 'tensors': [['C3', 'T3'], 'projector_right_top']}

Fig. 21 Contraction for C3 during right absorption.

ctmrg_absorption_right_C3_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,Zbed,Yced->ZY', 'filter_additional_tensors': ['projector_right_top'], 'filter_peps_tensors': [['C3_phase', 'T3']], 'ncon_network': [(1, 2), (-1, 1, 4, 3), (-2, 2, 4, 3)], 'network': [[(1, 2), (-1, 1, 4, 3)], (-2, 2, 4, 3)], 'network_additional_tensors': [(-2, 2, 4, 3)], 'network_peps_tensors': [[(1, 2), (-1, 1, 4, 3)]], 'tensors': [['C3_phase', 'T3'], 'projector_right_top']}

Fig. 22 Contraction for C3 during right absorption. Here C3 is the tensor with structure factor phase included which is grown by a normal T3 tensor.

ctmrg_absorption_right_C3_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,Zbed,Yced->ZY', 'filter_additional_tensors': ['projector_right_top'], 'filter_peps_tensors': [['C3', 'T3_phase']], 'ncon_network': [(1, 2), (-1, 1, 4, 3), (-2, 2, 4, 3)], 'network': [[(1, 2), (-1, 1, 4, 3)], (-2, 2, 4, 3)], 'network_additional_tensors': [(-2, 2, 4, 3)], 'network_peps_tensors': [[(1, 2), (-1, 1, 4, 3)]], 'tensors': [['C3', 'T3_phase'], 'projector_right_top']}

Fig. 23 Contraction for C3 during right absorption. Here C3 is the tensor with structure factor phase not included yet which is grown by a T3 tensor which includes a phase already.

ctmrg_absorption_right_T2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zigdc,Yjgfe,dfhb,Wbec,hjiX->ZYXW', 'filter_additional_tensors': ['projector_right_top', 'projector_right_bottom'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2']], 'ncon_network': [(-1, 8, 6, 3, 2), (-2, 9, 6, 5, 4), (3, 5, 7, 1), (-4, 1, 4, 2), (7, 9, 8, -3)], 'network': [[(-1, 8, 6, 3, 2), (-2, 9, 6, 5, 4), (3, 5, 7, 1)], (-4, 1, 4, 2), (7, 9, 8, -3)], 'network_additional_tensors': [(-4, 1, 4, 2), (7, 9, 8, -3)], 'network_peps_tensors': [[(-1, 8, 6, 3, 2), (-2, 9, 6, 5, 4), (3, 5, 7, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T2'], 'projector_right_top', 'projector_right_bottom']}

Fig. 24 Contraction for T2 during right absorption.

ctmrg_absorption_right_T2_large_d: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Ziced,Yjcgf,eghb,Wbfd,hjiX->ZYXW', 'filter_additional_tensors': ['projector_right_top', 'projector_right_bottom'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2']], 'ncon_network': [(-1, 8, 2, 4, 3), (-2, 9, 2, 6, 5), (4, 6, 7, 1), (-4, 1, 5, 3), (7, 9, 8, -3)], 'network': [[(-1, 8, 2, 4, 3), (-2, 9, 2, 6, 5), (4, 6, 7, 1)], (-4, 1, 5, 3), (7, 9, 8, -3)], 'network_additional_tensors': [(-4, 1, 5, 3), (7, 9, 8, -3)], 'network_peps_tensors': [[(-1, 8, 2, 4, 3), (-2, 9, 2, 6, 5), (4, 6, 7, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T2'], 'projector_right_top', 'projector_right_bottom']}

ctmrg_absorption_right_T2_large_d_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Ziced,Yjcgf,eghb,Wbfd,hjiX->ZYXW', 'filter_additional_tensors': ['projector_right_top', 'projector_right_bottom'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2_phase']], 'ncon_network': [(-1, 8, 2, 4, 3), (-2, 9, 2, 6, 5), (4, 6, 7, 1), (-4, 1, 5, 3), (7, 9, 8, -3)], 'network': [[(-1, 8, 2, 4, 3), (-2, 9, 2, 6, 5), (4, 6, 7, 1)], (-4, 1, 5, 3), (7, 9, 8, -3)], 'network_additional_tensors': [(-4, 1, 5, 3), (7, 9, 8, -3)], 'network_peps_tensors': [[(-1, 8, 2, 4, 3), (-2, 9, 2, 6, 5), (4, 6, 7, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T2_phase'], 'projector_right_top', 'projector_right_bottom']}

ctmrg_absorption_right_T2_large_d_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zjcfe,Ykdhg,fhib,Wbge,ikjX,cd->ZYXW', 'filter_additional_tensors': ['projector_right_top', 'projector_right_bottom', 'structure_factor_gate'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2']], 'ncon_network': [(-1, 9, 2, 5, 4), (-2, 10, 3, 7, 6), (5, 7, 8, 1), (-4, 1, 6, 4), (8, 10, 9, -3), (2, 3)], 'network': [[(-1, 9, 2, 5, 4), (-2, 10, 3, 7, 6), (5, 7, 8, 1)], (-4, 1, 6, 4), (8, 10, 9, -3), (2, 3)], 'network_additional_tensors': [(-4, 1, 6, 4), (8, 10, 9, -3), (2, 3)], 'network_peps_tensors': [[(-1, 9, 2, 5, 4), (-2, 10, 3, 7, 6), (5, 7, 8, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T2'], 'projector_right_top', 'projector_right_bottom', 'structure_factor_gate']}

ctmrg_absorption_top_C1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zedb,bc,cdeY->ZY', 'filter_additional_tensors': ['projector_top_right'], 'filter_peps_tensors': [['T4', 'C1']], 'ncon_network': [(-1, 4, 3, 1), (1, 2), (2, 3, 4, -2)], 'network': [[(-1, 4, 3, 1), (1, 2)], (2, 3, 4, -2)], 'network_additional_tensors': [(2, 3, 4, -2)], 'network_peps_tensors': [[(-1, 4, 3, 1), (1, 2)]], 'tensors': [['T4', 'C1'], 'projector_top_right']}

Fig. 25 Contraction for C1 during top absorption.

ctmrg_absorption_top_C1_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zedb,bc,cdeY->ZY', 'filter_additional_tensors': ['projector_top_right'], 'filter_peps_tensors': [['T4', 'C1_phase']], 'ncon_network': [(-1, 4, 3, 1), (1, 2), (2, 3, 4, -2)], 'network': [[(-1, 4, 3, 1), (1, 2)], (2, 3, 4, -2)], 'network_additional_tensors': [(2, 3, 4, -2)], 'network_peps_tensors': [[(-1, 4, 3, 1), (1, 2)]], 'tensors': [['T4', 'C1_phase'], 'projector_top_right']}

Fig. 26 Contraction for C1 during top absorption. Here C1 is the tensor with structure factor phase included which is grown by a normal T4 tensor.

ctmrg_absorption_top_C1_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zedb,bc,cdeY->ZY', 'filter_additional_tensors': ['projector_top_right'], 'filter_peps_tensors': [['T4_phase', 'C1']], 'ncon_network': [(-1, 4, 3, 1), (1, 2), (2, 3, 4, -2)], 'network': [[(-1, 4, 3, 1), (1, 2)], (2, 3, 4, -2)], 'network_additional_tensors': [(2, 3, 4, -2)], 'network_peps_tensors': [[(-1, 4, 3, 1), (1, 2)]], 'tensors': [['T4_phase', 'C1'], 'projector_top_right']}

Fig. 27 Contraction for C1 during top absorption. Here C1 is the tensor with structure factor phase not included yet which is grown by a T4 tensor which includes a phase already.

ctmrg_absorption_top_C2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,deYb,Zcde->ZY', 'filter_additional_tensors': ['projector_top_left'], 'filter_peps_tensors': [['C2', 'T2']], 'ncon_network': [(2, 1), (3, 4, -2, 1), (-1, 2, 3, 4)], 'network': [[(2, 1), (3, 4, -2, 1)], (-1, 2, 3, 4)], 'network_additional_tensors': [(-1, 2, 3, 4)], 'network_peps_tensors': [[(2, 1), (3, 4, -2, 1)]], 'tensors': [['C2', 'T2'], 'projector_top_left']}

Fig. 28 Contraction for C2 during top absorption.

ctmrg_absorption_top_C2_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,deYb,Zcde->ZY', 'filter_additional_tensors': ['projector_top_left'], 'filter_peps_tensors': [['C2_phase', 'T2']], 'ncon_network': [(2, 1), (3, 4, -2, 1), (-1, 2, 3, 4)], 'network': [[(2, 1), (3, 4, -2, 1)], (-1, 2, 3, 4)], 'network_additional_tensors': [(-1, 2, 3, 4)], 'network_peps_tensors': [[(2, 1), (3, 4, -2, 1)]], 'tensors': [['C2_phase', 'T2'], 'projector_top_left']}

Fig. 29 Contraction for C2 during top absorption. Here C2 is the tensor with structure factor phase included which is grown by a normal T2 tensor.

ctmrg_absorption_top_C2_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,deYb,Zcde->ZY', 'filter_additional_tensors': ['projector_top_left'], 'filter_peps_tensors': [['C2', 'T2_phase']], 'ncon_network': [(2, 1), (3, 4, -2, 1), (-1, 2, 3, 4)], 'network': [[(2, 1), (3, 4, -2, 1)], (-1, 2, 3, 4)], 'network_additional_tensors': [(-1, 2, 3, 4)], 'network_peps_tensors': [[(2, 1), (3, 4, -2, 1)]], 'tensors': [['C2', 'T2_phase'], 'projector_top_left']}

Fig. 30 Contraction for C2 during top absorption. Here C2 is the tensor with structure factor phase not included yet which is grown by a T2 tensor which includes a phase already.

ctmrg_absorption_top_T1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dYgic,fXgje,bceh,Zbdf,hijW->ZYXW', 'filter_additional_tensors': ['projector_top_left', 'projector_top_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1']], 'ncon_network': [(3, -2, 6, 8, 2), (5, -3, 6, 9, 4), (1, 2, 4, 7), (-1, 1, 3, 5), (7, 8, 9, -4)], 'network': [[(3, -2, 6, 8, 2), (5, -3, 6, 9, 4), (1, 2, 4, 7)], (-1, 1, 3, 5), (7, 8, 9, -4)], 'network_additional_tensors': [(-1, 1, 3, 5), (7, 8, 9, -4)], 'network_peps_tensors': [[(3, -2, 6, 8, 2), (5, -3, 6, 9, 4), (1, 2, 4, 7)]], 'tensors': [['tensor', 'tensor_conj', 'T1'], 'projector_top_left', 'projector_top_right']}

Fig. 31 Contraction for T1 during top absorption.

ctmrg_absorption_top_T1_large_d: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eYcid,gXcjf,bdfh,Zbeg,hijW->ZYXW', 'filter_additional_tensors': ['projector_top_left', 'projector_top_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1']], 'ncon_network': [(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (1, 3, 5, 7), (-1, 1, 4, 6), (7, 8, 9, -4)], 'network': [[(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (1, 3, 5, 7)], (-1, 1, 4, 6), (7, 8, 9, -4)], 'network_additional_tensors': [(-1, 1, 4, 6), (7, 8, 9, -4)], 'network_peps_tensors': [[(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (1, 3, 5, 7)]], 'tensors': [['tensor', 'tensor_conj', 'T1'], 'projector_top_left', 'projector_top_right']}

ctmrg_absorption_top_T1_large_d_phase_1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eYcid,gXcjf,bdfh,Zbeg,hijW->ZYXW', 'filter_additional_tensors': ['projector_top_left', 'projector_top_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1_phase']], 'ncon_network': [(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (1, 3, 5, 7), (-1, 1, 4, 6), (7, 8, 9, -4)], 'network': [[(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (1, 3, 5, 7)], (-1, 1, 4, 6), (7, 8, 9, -4)], 'network_additional_tensors': [(-1, 1, 4, 6), (7, 8, 9, -4)], 'network_peps_tensors': [[(4, -2, 2, 8, 3), (6, -3, 2, 9, 5), (1, 3, 5, 7)]], 'tensors': [['tensor', 'tensor_conj', 'T1_phase'], 'projector_top_left', 'projector_top_right']}

ctmrg_absorption_top_T1_large_d_phase_2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fYcje,hXdkg,begi,Zbfh,ijkW,cd->ZYXW', 'filter_additional_tensors': ['projector_top_left', 'projector_top_right', 'structure_factor_gate'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1']], 'ncon_network': [(5, -2, 2, 9, 4), (7, -3, 3, 10, 6), (1, 4, 6, 8), (-1, 1, 5, 7), (8, 9, 10, -4), (2, 3)], 'network': [[(5, -2, 2, 9, 4), (7, -3, 3, 10, 6), (1, 4, 6, 8)], (-1, 1, 5, 7), (8, 9, 10, -4), (2, 3)], 'network_additional_tensors': [(-1, 1, 5, 7), (8, 9, 10, -4), (2, 3)], 'network_peps_tensors': [[(5, -2, 2, 9, 4), (7, -3, 3, 10, 6), (1, 4, 6, 8)]], 'tensors': [['tensor', 'tensor_conj', 'T1'], 'projector_top_left', 'projector_top_right', 'structure_factor_gate']}

ctmrg_bottom_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dehXV,fghYU,cZge,cb,bfdW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3', 'C4', 'T4']], 'ncon_network': [(3, 4, 7, -3, -5), (5, 6, 7, -2, -6), (2, -1, 6, 4), (2, 1), (1, 5, 3, -4)], 'network': [[(3, 4, 7, -3, -5), (5, 6, 7, -2, -6), (2, -1, 6, 4), (2, 1), (1, 5, 3, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 7, -3, -5), (5, 6, 7, -2, -6), (2, -1, 6, 4), (2, 1), (1, 5, 3, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T3', 'C4', 'T4']]}

Fig. 32 Contraction for bottom left CTM corner.

ctmrg_bottom_left_large_d: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efdXV,ghdYU,cZhf,cb,bgeW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3', 'C4', 'T4']], 'ncon_network': [(4, 5, 3, -3, -5), (6, 7, 3, -2, -6), (2, -1, 7, 5), (2, 1), (1, 6, 4, -4)], 'network': [[(4, 5, 3, -3, -5), (6, 7, 3, -2, -6), (2, -1, 7, 5), (2, 1), (1, 6, 4, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, 3, -3, -5), (6, 7, 3, -2, -6), (2, -1, 7, 5), (2, 1), (1, 6, 4, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T3', 'C4', 'T4']]}

Fig. 33 Contraction for bottom left CTM corner for high physical dimensions.

ctmrg_bottom_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'UdheX,VfhgY,egcZ,Wbfd,bc->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2', 'T3', 'C3']], 'ncon_network': [(-6, 3, 7, 4, -3), (-5, 5, 7, 6, -2), (4, 6, 2, -1), (-4, 1, 5, 3), (1, 2)], 'network': [[(-6, 3, 7, 4, -3), (-5, 5, 7, 6, -2), (4, 6, 2, -1), (-4, 1, 5, 3), (1, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-6, 3, 7, 4, -3), (-5, 5, 7, 6, -2), (4, 6, 2, -1), (-4, 1, 5, 3), (1, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T2', 'T3', 'C3']]}

Fig. 34 Contraction for bottom right CTM corner.

ctmrg_bottom_right_large_d: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'UedfX,VgdhY,fhcZ,Wbge,bc->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2', 'T3', 'C3']], 'ncon_network': [(-6, 4, 3, 5, -3), (-5, 6, 3, 7, -2), (5, 7, 2, -1), (-4, 1, 6, 4), (1, 2)], 'network': [[(-6, 4, 3, 5, -3), (-5, 6, 3, 7, -2), (5, 7, 2, -1), (-4, 1, 6, 4), (1, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-6, 4, 3, 5, -3), (-5, 6, 3, 7, -2), (5, 7, 2, -1), (-4, 1, 6, 4), (1, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T2', 'T3', 'C3']]}

Fig. 35 Contraction for bottom right CTM corner for high physical dimensions.

ctmrg_gauge_fix_C2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,Zb,Yc->ZY', 'filter_additional_tensors': ['left_unitary', 'bottom_unitary'], 'filter_peps_tensors': [['C2']], 'ncon_network': [(1, 2), (-1, 1), (-2, 2)], 'network': [[(1, 2)], (-1, 1), (-2, 2)], 'network_additional_tensors': [(-1, 1), (-2, 2)], 'network_peps_tensors': [[(1, 2)]], 'tensors': [['C2'], 'left_unitary', 'bottom_unitary']}

ctmrg_gauge_fix_C4: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,cY,bZ->ZY', 'filter_additional_tensors': ['top_unitary', 'right_unitary'], 'filter_peps_tensors': [['C4']], 'ncon_network': [(1, 2), (2, -2), (1, -1)], 'network': [[(1, 2)], (2, -2), (1, -1)], 'network_additional_tensors': [(2, -2), (1, -1)], 'network_peps_tensors': [[(1, 2)]], 'tensors': [['C4'], 'top_unitary', 'right_unitary']}

ctmrg_gauge_fix_T1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bYXc,Zb,Wc->ZYXW', 'filter_additional_tensors': ['left_unitary', 'right_unitary'], 'filter_peps_tensors': [['T1']], 'ncon_network': [(1, -2, -3, 2), (-1, 1), (-4, 2)], 'network': [[(1, -2, -3, 2)], (-1, 1), (-4, 2)], 'network_additional_tensors': [(-1, 1), (-4, 2)], 'network_peps_tensors': [[(1, -2, -3, 2)]], 'tensors': [['T1'], 'left_unitary', 'right_unitary']}

ctmrg_gauge_fix_T2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ZYbc,Wc,Xb->ZYXW', 'filter_additional_tensors': ['top_unitary', 'bottom_unitary'], 'filter_peps_tensors': [['T2']], 'ncon_network': [(-1, -2, 1, 2), (-4, 2), (-3, 1)], 'network': [[(-1, -2, 1, 2)], (-4, 2), (-3, 1)], 'network_additional_tensors': [(-4, 2), (-3, 1)], 'network_peps_tensors': [[(-1, -2, 1, 2)]], 'tensors': [['T2'], 'top_unitary', 'bottom_unitary']}

ctmrg_gauge_fix_T3: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bcXW,bZ,cY->ZYXW', 'filter_additional_tensors': ['left_unitary', 'right_unitary'], 'filter_peps_tensors': [['T3']], 'ncon_network': [(1, 2, -3, -4), (1, -1), (2, -2)], 'network': [[(1, 2, -3, -4)], (1, -1), (2, -2)], 'network_additional_tensors': [(1, -1), (2, -2)], 'network_peps_tensors': [[(1, 2, -3, -4)]], 'tensors': [['T3'], 'left_unitary', 'right_unitary']}

ctmrg_gauge_fix_T4: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bYXc,cW,bZ->ZYXW', 'filter_additional_tensors': ['top_unitary', 'bottom_unitary'], 'filter_peps_tensors': [['T4']], 'ncon_network': [(1, -2, -3, 2), (2, -4), (1, -1)], 'network': [[(1, -2, -3, 2)], (2, -4), (1, -1)], 'network_additional_tensors': [(2, -4), (1, -1)], 'network_peps_tensors': [[(1, -2, -3, 2)]], 'tensors': [['T4'], 'top_unitary', 'bottom_unitary']}

ctmrg_split_transfer_absorption_bottom_C3: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'egY,bde,cb,fgZ,cdf->ZY', 'filter_additional_tensors': ['projector_bottom_left_ket', 'projector_bottom_left_bra'], 'filter_peps_tensors': [['T2_ket', 'T2_bra', 'C3']], 'ncon_network': [(4, 6, -2), (1, 3, 4), (2, 1), (5, 6, -1), (2, 3, 5)], 'network': [[(4, 6, -2), (1, 3, 4), (2, 1)], (5, 6, -1), (2, 3, 5)], 'network_additional_tensors': [(5, 6, -1), (2, 3, 5)], 'network_peps_tensors': [[(4, 6, -2), (1, 3, 4), (2, 1)]], 'tensors': [['T2_ket', 'T2_bra', 'C3'], 'projector_bottom_left_ket', 'projector_bottom_left_bra']}

ctmrg_split_transfer_absorption_bottom_C4: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,egY,bde,Zfg,fcd->ZY', 'filter_additional_tensors': ['projector_bottom_right_ket', 'projector_bottom_right_bra'], 'filter_peps_tensors': [['C4', 'T4_ket', 'T4_bra']], 'ncon_network': [(2, 1), (4, 6, -2), (1, 3, 4), (-1, 5, 6), (5, 2, 3)], 'network': [[(2, 1), (4, 6, -2), (1, 3, 4)], (-1, 5, 6), (5, 2, 3)], 'network_additional_tensors': [(-1, 5, 6), (5, 2, 3)], 'network_peps_tensors': [[(2, 1), (4, 6, -2), (1, 3, 4)]], 'tensors': [['C4', 'T4_ket', 'T4_bra'], 'projector_bottom_right_ket', 'projector_bottom_right_bra']}

ctmrg_split_transfer_absorption_bottom_T3: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'mjkiY,gekdX,cjf,feb,lmZ,cgl,Whi,hbd->ZYXW', 'filter_additional_tensors': ['projector_bottom_left_ket', 'projector_bottom_left_bra', 'projector_bottom_right_ket', 'projector_bottom_right_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3_ket', 'T3_bra']], 'ncon_network': [(12, 9, 10, 8, -2), (6, 4, 10, 3, -3), (2, 9, 5), (5, 4, 1), (11, 12, -1), (2, 6, 11), (-4, 7, 8), (7, 1, 3)], 'network': [[(12, 9, 10, 8, -2), (6, 4, 10, 3, -3), (2, 9, 5), (5, 4, 1)], (11, 12, -1), (2, 6, 11), (-4, 7, 8), (7, 1, 3)], 'network_additional_tensors': [(11, 12, -1), (2, 6, 11), (-4, 7, 8), (7, 1, 3)], 'network_peps_tensors': [[(12, 9, 10, 8, -2), (6, 4, 10, 3, -3), (2, 9, 5), (5, 4, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T3_ket', 'T3_bra'], 'projector_bottom_left_ket', 'projector_bottom_left_bra', 'projector_bottom_right_ket', 'projector_bottom_right_bra']}

ctmrg_split_transfer_absorption_bottom_T3_bra: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fdhcY,edb,gjhZ,efg,Xij,ibc->ZYX', 'filter_additional_tensors': ['projector_bottom_left_phys_ket', 'projector_bottom_left_phys_bra', 'projector_bottom_right_ket', 'projector_bottom_right_bra'], 'filter_peps_tensors': [['tensor_conj', 'T3_bra']], 'ncon_network': [(5, 3, 7, 2, -2), (4, 3, 1), (6, 9, 7, -1), (4, 5, 6), (-3, 8, 9), (8, 1, 2)], 'network': [[(5, 3, 7, 2, -2), (4, 3, 1)], (6, 9, 7, -1), (4, 5, 6), (-3, 8, 9), (8, 1, 2)], 'network_additional_tensors': [(6, 9, 7, -1), (4, 5, 6), (-3, 8, 9), (8, 1, 2)], 'network_peps_tensors': [[(5, 3, 7, 2, -2), (4, 3, 1)]], 'tensors': [['tensor_conj', 'T3_bra'], 'projector_bottom_left_phys_ket', 'projector_bottom_left_phys_bra', 'projector_bottom_right_ket', 'projector_bottom_right_bra']}

ctmrg_split_transfer_absorption_bottom_T3_ket: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'jghfY,cgb,ijZ,cdi,Xefh,ebd->ZYX', 'filter_additional_tensors': ['projector_bottom_left_ket', 'projector_bottom_left_bra', 'projector_bottom_right_phys_ket', 'projector_bottom_right_phys_bra'], 'filter_peps_tensors': [['tensor', 'T3_ket']], 'ncon_network': [(9, 6, 7, 5, -2), (2, 6, 1), (8, 9, -1), (2, 3, 8), (-3, 4, 5, 7), (4, 1, 3)], 'network': [[(9, 6, 7, 5, -2), (2, 6, 1)], (8, 9, -1), (2, 3, 8), (-3, 4, 5, 7), (4, 1, 3)], 'network_additional_tensors': [(8, 9, -1), (2, 3, 8), (-3, 4, 5, 7), (4, 1, 3)], 'network_peps_tensors': [[(9, 6, 7, 5, -2), (2, 6, 1)]], 'tensors': [['tensor', 'T3_ket'], 'projector_bottom_left_ket', 'projector_bottom_left_bra', 'projector_bottom_right_phys_ket', 'projector_bottom_right_phys_bra']}

ctmrg_split_transfer_absorption_left_C1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,bde,egY,fcd,Zfg->ZY', 'filter_additional_tensors': ['projector_left_bottom_ket', 'projector_left_bottom_bra'], 'filter_peps_tensors': [['C1', 'T1_ket', 'T1_bra']], 'ncon_network': [(2, 1), (1, 3, 4), (4, 6, -2), (5, 2, 3), (-1, 5, 6)], 'network': [[(2, 1), (1, 3, 4), (4, 6, -2)], (5, 2, 3), (-1, 5, 6)], 'network_additional_tensors': [(5, 2, 3), (-1, 5, 6)], 'network_peps_tensors': [[(2, 1), (1, 3, 4), (4, 6, -2)]], 'tensors': [['C1', 'T1_ket', 'T1_bra'], 'projector_left_bottom_ket', 'projector_left_bottom_bra']}

ctmrg_split_transfer_absorption_left_C4: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bde,egZ,bc,cdf,fgY->ZY', 'filter_additional_tensors': ['projector_left_top_ket', 'projector_left_top_bra'], 'filter_peps_tensors': [['T3_ket', 'T3_bra', 'C4']], 'ncon_network': [(1, 3, 4), (4, 6, -1), (1, 2), (2, 3, 5), (5, 6, -2)], 'network': [[(1, 3, 4), (4, 6, -1), (1, 2)], (2, 3, 5), (5, 6, -2)], 'network_additional_tensors': [(2, 3, 5), (5, 6, -2)], 'network_peps_tensors': [[(1, 3, 4), (4, 6, -1), (1, 2)]], 'tensors': [['T3_ket', 'T3_bra', 'C4'], 'projector_left_top_ket', 'projector_left_top_bra']}

ctmrg_split_transfer_absorption_left_T4: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'egkXd,jmkYi,feb,cjf,bdh,hiW,lcg,Zlm->ZYXW', 'filter_additional_tensors': ['projector_left_top_ket', 'projector_left_top_bra', 'projector_left_bottom_ket', 'projector_left_bottom_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4_ket', 'T4_bra']], 'ncon_network': [(4, 6, 10, -3, 3), (9, 12, 10, -2, 8), (5, 4, 1), (2, 9, 5), (1, 3, 7), (7, 8, -4), (11, 2, 6), (-1, 11, 12)], 'network': [[(4, 6, 10, -3, 3), (9, 12, 10, -2, 8), (5, 4, 1), (2, 9, 5)], (1, 3, 7), (7, 8, -4), (11, 2, 6), (-1, 11, 12)], 'network_additional_tensors': [(1, 3, 7), (7, 8, -4), (11, 2, 6), (-1, 11, 12)], 'network_peps_tensors': [[(4, 6, 10, -3, 3), (9, 12, 10, -2, 8), (5, 4, 1), (2, 9, 5)]], 'tensors': [['tensor', 'tensor_conj', 'T4_ket', 'T4_bra'], 'projector_left_top_ket', 'projector_left_top_bra', 'projector_left_bottom_ket', 'projector_left_bottom_bra']}

ctmrg_split_transfer_absorption_left_T4_bra: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'gjhYf,cgb,bde,efhX,icd,Zij->ZYX', 'filter_additional_tensors': ['projector_left_top_phys_ket', 'projector_left_top_phys_bra', 'projector_left_bottom_ket', 'projector_left_bottom_bra'], 'filter_peps_tensors': [['tensor_conj', 'T4_bra']], 'ncon_network': [(6, 9, 7, -2, 5), (2, 6, 1), (1, 3, 4), (4, 5, 7, -3), (8, 2, 3), (-1, 8, 9)], 'network': [[(6, 9, 7, -2, 5), (2, 6, 1)], (1, 3, 4), (4, 5, 7, -3), (8, 2, 3), (-1, 8, 9)], 'network_additional_tensors': [(1, 3, 4), (4, 5, 7, -3), (8, 2, 3), (-1, 8, 9)], 'network_peps_tensors': [[(6, 9, 7, -2, 5), (2, 6, 1)]], 'tensors': [['tensor_conj', 'T4_bra'], 'projector_left_top_phys_ket', 'projector_left_top_phys_bra', 'projector_left_bottom_ket', 'projector_left_bottom_bra']}

ctmrg_split_transfer_absorption_left_T4_ket: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dfhYc,edb,bci,ijX,gef,Zgjh->ZYX', 'filter_additional_tensors': ['projector_left_top_ket', 'projector_left_top_bra', 'projector_left_bottom_phys_ket', 'projector_left_bottom_phys_bra'], 'filter_peps_tensors': [['tensor', 'T4_ket']], 'ncon_network': [(3, 5, 7, -2, 2), (4, 3, 1), (1, 2, 8), (8, 9, -3), (6, 4, 5), (-1, 6, 9, 7)], 'network': [[(3, 5, 7, -2, 2), (4, 3, 1)], (1, 2, 8), (8, 9, -3), (6, 4, 5), (-1, 6, 9, 7)], 'network_additional_tensors': [(1, 2, 8), (8, 9, -3), (6, 4, 5), (-1, 6, 9, 7)], 'network_peps_tensors': [[(3, 5, 7, -2, 2), (4, 3, 1)]], 'tensors': [['tensor', 'T4_ket'], 'projector_left_top_ket', 'projector_left_top_bra', 'projector_left_bottom_phys_ket', 'projector_left_bottom_phys_bra']}

ctmrg_split_transfer_absorption_right_C2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zge,edb,bc,fgY,cdf->ZY', 'filter_additional_tensors': ['projector_right_bottom_ket', 'projector_right_bottom_bra'], 'filter_peps_tensors': [['T1_ket', 'T1_bra', 'C2']], 'ncon_network': [(-1, 6, 4), (4, 3, 1), (1, 2), (5, 6, -2), (2, 3, 5)], 'network': [[(-1, 6, 4), (4, 3, 1), (1, 2)], (5, 6, -2), (2, 3, 5)], 'network_additional_tensors': [(5, 6, -2), (2, 3, 5)], 'network_peps_tensors': [[(-1, 6, 4), (4, 3, 1), (1, 2)]], 'tensors': [['T1_ket', 'T1_bra', 'C2'], 'projector_right_bottom_ket', 'projector_right_bottom_bra']}

ctmrg_split_transfer_absorption_right_C3: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,Zge,edb,Yfg,fcd->ZY', 'filter_additional_tensors': ['projector_right_top_ket', 'projector_right_top_bra'], 'filter_peps_tensors': [['C3', 'T3_ket', 'T3_bra']], 'ncon_network': [(1, 2), (-1, 6, 4), (4, 3, 1), (-2, 5, 6), (5, 2, 3)], 'network': [[(1, 2), (-1, 6, 4), (4, 3, 1)], (-2, 5, 6), (5, 2, 3)], 'network_additional_tensors': [(-2, 5, 6), (5, 2, 3)], 'network_peps_tensors': [[(1, 2), (-1, 6, 4), (4, 3, 1)]], 'tensors': [['C3', 'T3_ket', 'T3_bra'], 'projector_right_top_ket', 'projector_right_top_bra']}

ctmrg_split_transfer_absorption_right_T2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Xikjm,Ydkeg,fjc,bef,Wlm,lcg,hiZ,bdh->ZYXW', 'filter_additional_tensors': ['projector_right_top_ket', 'projector_right_top_bra', 'projector_right_bottom_ket', 'projector_right_bottom_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2_ket', 'T2_bra']], 'ncon_network': [(-3, 8, 10, 9, 12), (-2, 3, 10, 4, 6), (5, 9, 2), (1, 4, 5), (-4, 11, 12), (11, 2, 6), (7, 8, -1), (1, 3, 7)], 'network': [[(-3, 8, 10, 9, 12), (-2, 3, 10, 4, 6), (5, 9, 2), (1, 4, 5)], (-4, 11, 12), (11, 2, 6), (7, 8, -1), (1, 3, 7)], 'network_additional_tensors': [(-4, 11, 12), (11, 2, 6), (7, 8, -1), (1, 3, 7)], 'network_peps_tensors': [[(-3, 8, 10, 9, 12), (-2, 3, 10, 4, 6), (5, 9, 2), (1, 4, 5)]], 'tensors': [['tensor', 'tensor_conj', 'T2_ket', 'T2_bra'], 'projector_right_top_ket', 'projector_right_top_bra', 'projector_right_bottom_ket', 'projector_right_bottom_bra']}

ctmrg_split_transfer_absorption_right_T2_bra: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Ychdf,bde,Xgjh,gef,ijZ,bci->ZYX', 'filter_additional_tensors': ['projector_right_top_phys_ket', 'projector_right_top_phys_bra', 'projector_right_bottom_ket', 'projector_right_bottom_bra'], 'filter_peps_tensors': [['tensor_conj', 'T2_bra']], 'ncon_network': [(-2, 2, 7, 3, 5), (1, 3, 4), (-3, 6, 9, 7), (6, 4, 5), (8, 9, -1), (1, 2, 8)], 'network': [[(-2, 2, 7, 3, 5), (1, 3, 4)], (-3, 6, 9, 7), (6, 4, 5), (8, 9, -1), (1, 2, 8)], 'network_additional_tensors': [(-3, 6, 9, 7), (6, 4, 5), (8, 9, -1), (1, 2, 8)], 'network_peps_tensors': [[(-2, 2, 7, 3, 5), (1, 3, 4)]], 'tensors': [['tensor_conj', 'T2_bra'], 'projector_right_top_phys_ket', 'projector_right_top_phys_bra', 'projector_right_bottom_ket', 'projector_right_bottom_bra']}

ctmrg_split_transfer_absorption_right_T2_ket: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Yfhgj,bgc,Xij,icd,efhZ,bde->ZYX', 'filter_additional_tensors': ['projector_right_top_ket', 'projector_right_top_bra', 'projector_right_bottom_phys_ket', 'projector_right_bottom_phys_bra'], 'filter_peps_tensors': [['tensor', 'T2_ket']], 'ncon_network': [(-2, 5, 7, 6, 9), (1, 6, 2), (-3, 8, 9), (8, 2, 3), (4, 5, 7, -1), (1, 3, 4)], 'network': [[(-2, 5, 7, 6, 9), (1, 6, 2)], (-3, 8, 9), (8, 2, 3), (4, 5, 7, -1), (1, 3, 4)], 'network_additional_tensors': [(-3, 8, 9), (8, 2, 3), (4, 5, 7, -1), (1, 3, 4)], 'network_peps_tensors': [[(-2, 5, 7, 6, 9), (1, 6, 2)]], 'tensors': [['tensor', 'T2_ket'], 'projector_right_top_ket', 'projector_right_top_bra', 'projector_right_bottom_phys_ket', 'projector_right_bottom_phys_bra']}

ctmrg_split_transfer_absorption_top_C1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'edb,Zge,bc,cdf,fgY->ZY', 'filter_additional_tensors': ['projector_top_right_ket', 'projector_top_right_bra'], 'filter_peps_tensors': [['T4_ket', 'T4_bra', 'C1']], 'ncon_network': [(4, 3, 1), (-1, 6, 4), (1, 2), (2, 3, 5), (5, 6, -2)], 'network': [[(4, 3, 1), (-1, 6, 4), (1, 2)], (2, 3, 5), (5, 6, -2)], 'network_additional_tensors': [(2, 3, 5), (5, 6, -2)], 'network_peps_tensors': [[(4, 3, 1), (-1, 6, 4), (1, 2)]], 'tensors': [['T4_ket', 'T4_bra', 'C1'], 'projector_top_right_ket', 'projector_top_right_bra']}

ctmrg_split_transfer_absorption_top_C2: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,edb,Yge,fcd,Zfg->ZY', 'filter_additional_tensors': ['projector_top_left_ket', 'projector_top_left_bra'], 'filter_peps_tensors': [['C2', 'T2_ket', 'T2_bra']], 'ncon_network': [(2, 1), (4, 3, 1), (-2, 6, 4), (5, 2, 3), (-1, 5, 6)], 'network': [[(2, 1), (4, 3, 1), (-2, 6, 4)], (5, 2, 3), (-1, 5, 6)], 'network_additional_tensors': [(5, 2, 3), (-1, 5, 6)], 'network_peps_tensors': [[(2, 1), (4, 3, 1), (-2, 6, 4)]], 'tensors': [['C2', 'T2_ket', 'T2_bra'], 'projector_top_left_ket', 'projector_top_left_bra']}

ctmrg_split_transfer_absorption_top_T1: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dYkge,iXkmj,bef,fjc,hbd,Zhi,cgl,lmW->ZYXW', 'filter_additional_tensors': ['projector_top_left_ket', 'projector_top_left_bra', 'projector_top_right_ket', 'projector_top_right_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1_ket', 'T1_bra']], 'ncon_network': [(3, -2, 10, 6, 4), (8, -3, 10, 12, 9), (1, 4, 5), (5, 9, 2), (7, 1, 3), (-1, 7, 8), (2, 6, 11), (11, 12, -4)], 'network': [[(3, -2, 10, 6, 4), (8, -3, 10, 12, 9), (1, 4, 5), (5, 9, 2)], (7, 1, 3), (-1, 7, 8), (2, 6, 11), (11, 12, -4)], 'network_additional_tensors': [(7, 1, 3), (-1, 7, 8), (2, 6, 11), (11, 12, -4)], 'network_peps_tensors': [[(3, -2, 10, 6, 4), (8, -3, 10, 12, 9), (1, 4, 5), (5, 9, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T1_ket', 'T1_bra'], 'projector_top_left_ket', 'projector_top_left_bra', 'projector_top_right_ket', 'projector_top_right_bra']}

ctmrg_split_transfer_absorption_top_T1_bra: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fYhjg,bgc,ebd,Zefh,cdi,ijX->ZYX', 'filter_additional_tensors': ['projector_top_left_phys_ket', 'projector_top_left_phys_bra', 'projector_top_right_ket', 'projector_top_right_bra'], 'filter_peps_tensors': [['tensor_conj', 'T1_bra']], 'ncon_network': [(5, -2, 7, 9, 6), (1, 6, 2), (4, 1, 3), (-1, 4, 5, 7), (2, 3, 8), (8, 9, -3)], 'network': [[(5, -2, 7, 9, 6), (1, 6, 2)], (4, 1, 3), (-1, 4, 5, 7), (2, 3, 8), (8, 9, -3)], 'network_additional_tensors': [(4, 1, 3), (-1, 4, 5, 7), (2, 3, 8), (8, 9, -3)], 'network_peps_tensors': [[(5, -2, 7, 9, 6), (1, 6, 2)]], 'tensors': [['tensor_conj', 'T1_bra'], 'projector_top_left_phys_ket', 'projector_top_left_phys_bra', 'projector_top_right_ket', 'projector_top_right_bra']}

ctmrg_split_transfer_absorption_top_T1_ket: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cYhfd,bde,ibc,Zij,efg,gjhX->ZYX', 'filter_additional_tensors': ['projector_top_left_ket', 'projector_top_left_bra', 'projector_top_right_phys_ket', 'projector_top_right_phys_bra'], 'filter_peps_tensors': [['tensor', 'T1_ket']], 'ncon_network': [(2, -2, 7, 5, 3), (1, 3, 4), (8, 1, 2), (-1, 8, 9), (4, 5, 6), (6, 9, 7, -3)], 'network': [[(2, -2, 7, 5, 3), (1, 3, 4)], (8, 1, 2), (-1, 8, 9), (4, 5, 6), (6, 9, 7, -3)], 'network_additional_tensors': [(8, 1, 2), (-1, 8, 9), (4, 5, 6), (6, 9, 7, -3)], 'network_peps_tensors': [[(2, -2, 7, 5, 3), (1, 3, 4)]], 'tensors': [['tensor', 'T1_ket'], 'projector_top_left_ket', 'projector_top_left_bra', 'projector_top_right_phys_ket', 'projector_top_right_phys_bra']}

ctmrg_split_transfer_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'olmkW,ifmgY,jkZ,egj,de,hfd,clh,cb,bin,noX->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2_ket', 'T2_bra', 'C3', 'T3_bra', 'T3_ket', 'C4', 'T4_bra', 'T4_ket']], 'ncon_network': [(14, 11, 12, 10, -4), (8, 5, 12, 6, -2), (9, 10, -1), (4, 6, 9), (3, 4), (7, 5, 3), (2, 11, 7), (2, 1), (1, 8, 13), (13, 14, -3)], 'network': [[(14, 11, 12, 10, -4), (8, 5, 12, 6, -2), (9, 10, -1), (4, 6, 9), (3, 4), (7, 5, 3), (2, 11, 7), (2, 1), (1, 8, 13), (13, 14, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(14, 11, 12, 10, -4), (8, 5, 12, 6, -2), (9, 10, -1), (4, 6, 9), (3, 4), (7, 5, 3), (2, 11, 7), (2, 1), (1, 8, 13), (13, 14, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T2_ket', 'T2_bra', 'C3', 'T3_bra', 'T3_ket', 'C4', 'T4_bra', 'T4_ket']]}

ctmrg_split_transfer_bottom_full: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'qsuzp,vwuyW,rqo,mvr,nm,nst,twx,zlkjY,yfkeh,xli,ifc,cd,deg,gjb,opX,Zbh->ZYXW', 'filter_additional_tensors': ['projector_left_top_ket', 'projector_right_top_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4_ket', 'T4_bra', 'C4', 'T3_ket', 'T3_bra'], ['tensor', 'tensor_conj', 'T3_ket', 'T3_bra', 'C3', 'T2_bra', 'T2_ket']], 'ncon_network': [(16, 18, 20, 25, 15), (21, 22, 20, 24, -4), (17, 16, 14), (12, 21, 17), (13, 12), (13, 18, 19), (19, 22, 23), (25, 11, 10, 9, -2), (24, 5, 10, 4, 7), (23, 11, 8), (8, 5, 2), (2, 3), (3, 4, 6), (6, 9, 1), (14, 15, -3), (-1, 1, 7)], 'network': [[(16, 18, 20, 25, 15), (21, 22, 20, 24, -4), (17, 16, 14), (12, 21, 17), (13, 12), (13, 18, 19), (19, 22, 23)], [(25, 11, 10, 9, -2), (24, 5, 10, 4, 7), (23, 11, 8), (8, 5, 2), (2, 3), (3, 4, 6), (6, 9, 1)], (14, 15, -3), (-1, 1, 7)], 'network_additional_tensors': [(14, 15, -3), (-1, 1, 7)], 'network_peps_tensors': [[(16, 18, 20, 25, 15), (21, 22, 20, 24, -4), (17, 16, 14), (12, 21, 17), (13, 12), (13, 18, 19), (19, 22, 23)], [(25, 11, 10, 9, -2), (24, 5, 10, 4, 7), (23, 11, 8), (8, 5, 2), (2, 3), (3, 4, 6), (6, 9, 1)]], 'tensors': [['tensor', 'tensor_conj', 'T4_ket', 'T4_bra', 'C4', 'T3_ket', 'T3_bra'], ['tensor', 'tensor_conj', 'T3_ket', 'T3_bra', 'C3', 'T2_bra', 'T2_ket'], 'projector_left_top_ket', 'projector_right_top_bra']}

ctmrg_split_transfer_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fimWg,lomYk,noZ,bin,bc,clh,hfd,de,egj,jkX->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3_bra', 'T3_ket', 'C4', 'T4_bra', 'T4_ket', 'C1', 'T1_ket', 'T1_bra']], 'ncon_network': [(5, 8, 12, -4, 6), (11, 14, 12, -2, 10), (13, 14, -1), (1, 8, 13), (1, 2), (2, 11, 7), (7, 5, 3), (3, 4), (4, 6, 9), (9, 10, -3)], 'network': [[(5, 8, 12, -4, 6), (11, 14, 12, -2, 10), (13, 14, -1), (1, 8, 13), (1, 2), (2, 11, 7), (7, 5, 3), (3, 4), (4, 6, 9), (9, 10, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 8, 12, -4, 6), (11, 14, 12, -2, 10), (13, 14, -1), (1, 8, 13), (1, 2), (2, 11, 7), (7, 5, 3), (3, 4), (4, 6, 9), (9, 10, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T3_bra', 'T3_ket', 'C4', 'T4_bra', 'T4_ket', 'C1', 'T1_ket', 'T1_bra']]}

ctmrg_split_transfer_left_bottom_half: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'finYg,mknjW,hfb,cmh,dc,dil,lke,bgX,Zej->ZYXW', 'filter_additional_tensors': ['projector_left_top_ket', 'projector_bottom_right_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4_ket', 'T4_bra', 'C4', 'T3_ket', 'T3_bra']], 'ncon_network': [(5, 8, 13, -2, 6), (12, 10, 13, 9, -4), (7, 5, 1), (2, 12, 7), (3, 2), (3, 8, 11), (11, 10, 4), (1, 6, -3), (-1, 4, 9)], 'network': [[(5, 8, 13, -2, 6), (12, 10, 13, 9, -4), (7, 5, 1), (2, 12, 7), (3, 2), (3, 8, 11), (11, 10, 4)], (1, 6, -3), (-1, 4, 9)], 'network_additional_tensors': [(1, 6, -3), (-1, 4, 9)], 'network_peps_tensors': [[(5, 8, 13, -2, 6), (12, 10, 13, 9, -4), (7, 5, 1), (2, 12, 7), (3, 2), (3, 8, 11), (11, 10, 4)]], 'tensors': [['tensor', 'tensor_conj', 'T4_ket', 'T4_bra', 'C4', 'T3_ket', 'T3_bra'], 'projector_left_top_ket', 'projector_bottom_right_bra']}

ctmrg_split_transfer_left_full: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eykhf,lzkWj,gjb,dfg,cd,iec,xli,wvuYy,squpz,twx,nst,mn,mvr,rqo,bhX,Zop->ZYXW', 'filter_additional_tensors': ['projector_top_right_ket', 'projector_bottom_right_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1_bra', 'T1_ket', 'C1', 'T4_ket', 'T4_bra'], ['tensor', 'tensor_conj', 'T4_ket', 'T4_bra', 'C4', 'T3_ket', 'T3_bra']], 'ncon_network': [(4, 24, 10, 7, 5), (11, 25, 10, -4, 9), (6, 9, 1), (3, 5, 6), (2, 3), (8, 4, 2), (23, 11, 8), (22, 21, 20, -2, 24), (18, 16, 20, 15, 25), (19, 22, 23), (13, 18, 19), (12, 13), (12, 21, 17), (17, 16, 14), (1, 7, -3), (-1, 14, 15)], 'network': [[(4, 24, 10, 7, 5), (11, 25, 10, -4, 9), (6, 9, 1), (3, 5, 6), (2, 3), (8, 4, 2), (23, 11, 8)], [(22, 21, 20, -2, 24), (18, 16, 20, 15, 25), (19, 22, 23), (13, 18, 19), (12, 13), (12, 21, 17), (17, 16, 14)], (1, 7, -3), (-1, 14, 15)], 'network_additional_tensors': [(1, 7, -3), (-1, 14, 15)], 'network_peps_tensors': [[(4, 24, 10, 7, 5), (11, 25, 10, -4, 9), (6, 9, 1), (3, 5, 6), (2, 3), (8, 4, 2), (23, 11, 8)], [(22, 21, 20, -2, 24), (18, 16, 20, 15, 25), (19, 22, 23), (13, 18, 19), (12, 13), (12, 21, 17), (17, 16, 14)]], 'tensors': [['tensor', 'tensor_conj', 'T1_bra', 'T1_ket', 'C1', 'T4_ket', 'T4_bra'], ['tensor', 'tensor_conj', 'T4_ket', 'T4_bra', 'C4', 'T3_ket', 'T3_bra'], 'projector_top_right_ket', 'projector_bottom_right_bra']}

ctmrg_split_transfer_left_top_half: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'finkg,lYnWm,blh,hfc,cd,dgj,jme,Zbi,ekX->ZYXW', 'filter_additional_tensors': ['projector_left_bottom_ket', 'projector_top_right_ket'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4_bra', 'T4_ket', 'C1', 'T1_ket', 'T1_bra']], 'ncon_network': [(5, 8, 13, 10, 6), (11, -2, 13, -4, 12), (1, 11, 7), (7, 5, 2), (2, 3), (3, 6, 9), (9, 12, 4), (-1, 1, 8), (4, 10, -3)], 'network': [[(5, 8, 13, 10, 6), (11, -2, 13, -4, 12), (1, 11, 7), (7, 5, 2), (2, 3), (3, 6, 9), (9, 12, 4)], (-1, 1, 8), (4, 10, -3)], 'network_additional_tensors': [(-1, 1, 8), (4, 10, -3)], 'network_peps_tensors': [[(5, 8, 13, 10, 6), (11, -2, 13, -4, 12), (1, 11, 7), (7, 5, 2), (2, 3), (3, 6, 9), (9, 12, 4)]], 'tensors': [['tensor', 'tensor_conj', 'T4_bra', 'T4_ket', 'C1', 'T1_ket', 'T1_bra'], 'projector_left_bottom_ket', 'projector_top_right_ket']}

ctmrg_split_transfer_phys_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'igXfY,bfZ,cb,hgc,dVh,de,eiW->ZYXWV', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor_conj', 'T2_bra', 'C3', 'T3_bra', 'T3_ket', 'C4', 'T4_bra']], 'ncon_network': [(8, 6, -3, 5, -2), (1, 5, -1), (2, 1), (7, 6, 2), (3, -5, 7), (3, 4), (4, 8, -4)], 'network': [[(8, 6, -3, 5, -2), (1, 5, -1), (2, 1), (7, 6, 2), (3, -5, 7), (3, 4), (4, 8, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(8, 6, -3, 5, -2), (1, 5, -1), (2, 1), (7, 6, 2), (3, -5, 7), (3, 4), (4, 8, -4)]], 'tensors': [['tensor_conj', 'T2_bra', 'C3', 'T3_bra', 'T3_ket', 'C4', 'T4_bra']]}

ctmrg_split_transfer_phys_bottom_full: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'noUqV,jnk,ij,ilm,mop,qeXdg,pYh,hec,cb,bdf,klW,Zfg->ZYXWVU', 'filter_additional_tensors': ['projector_left_top_phys', 'projector_right_top_phys'], 'filter_peps_tensors': [['tensor_conj', 'T4_bra', 'C4', 'T3_ket', 'T3_bra'], ['tensor_conj', 'T3_ket', 'T3_bra', 'C3', 'T2_bra']], 'ncon_network': [(13, 14, -6, 16, -5), (9, 13, 10), (8, 9), (8, 11, 12), (12, 14, 15), (16, 4, -3, 3, 6), (15, -2, 7), (7, 4, 2), (2, 1), (1, 3, 5), (10, 11, -4), (-1, 5, 6)], 'network': [[(13, 14, -6, 16, -5), (9, 13, 10), (8, 9), (8, 11, 12), (12, 14, 15)], [(16, 4, -3, 3, 6), (15, -2, 7), (7, 4, 2), (2, 1), (1, 3, 5)], (10, 11, -4), (-1, 5, 6)], 'network_additional_tensors': [(10, 11, -4), (-1, 5, 6)], 'network_peps_tensors': [[(13, 14, -6, 16, -5), (9, 13, 10), (8, 9), (8, 11, 12), (12, 14, 15)], [(16, 4, -3, 3, 6), (15, -2, 7), (7, 4, 2), (2, 1), (1, 3, 5)]], 'tensors': [['tensor_conj', 'T4_bra', 'C4', 'T3_ket', 'T3_bra'], ['tensor_conj', 'T3_ket', 'T3_bra', 'C3', 'T2_bra'], 'projector_left_top_phys', 'projector_right_top_phys']}

ctmrg_split_transfer_phys_bottom_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'feWYU,dfV,cXd,bc,beZ->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'T4_ket', 'T4_bra', 'C4', 'T3_ket']], 'ncon_network': [(5, 4, -4, -2, -6), (3, 5, -5), (2, -3, 3), (1, 2), (1, 4, -1)], 'network': [[(5, 4, -4, -2, -6), (3, 5, -5), (2, -3, 3), (1, 2), (1, 4, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 4, -4, -2, -6), (3, 5, -5), (2, -3, 3), (1, 2), (1, 4, -1)]], 'tensors': [['tensor', 'T4_ket', 'T4_bra', 'C4', 'T3_ket']]}

ctmrg_split_transfer_phys_bottom_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'VeUdY,Xec,cb,bdf,fWZ->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor_conj', 'T3_bra', 'C3', 'T2_bra', 'T2_ket']], 'ncon_network': [(-5, 4, -6, 3, -2), (-3, 4, 2), (2, 1), (1, 3, 5), (5, -4, -1)], 'network': [[(-5, 4, -6, 3, -2), (-3, 4, 2), (2, 1), (1, 3, 5), (5, -4, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-5, 4, -6, 3, -2), (-3, 4, 2), (2, 1), (1, 3, 5), (5, -4, -1)]], 'tensors': [['tensor_conj', 'T3_bra', 'C3', 'T2_bra', 'T2_ket']]}

ctmrg_split_transfer_phys_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'giXVf,eiZ,ed,dYh,hgc,cb,bfW->ZYXWV', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'T3_ket', 'C4', 'T4_bra', 'T4_ket', 'C1', 'T1_ket']], 'ncon_network': [(6, 8, -3, -5, 5), (4, 8, -1), (4, 3), (3, -2, 7), (7, 6, 2), (2, 1), (1, 5, -4)], 'network': [[(6, 8, -3, -5, 5), (4, 8, -1), (4, 3), (3, -2, 7), (7, 6, 2), (2, 1), (1, 5, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 8, -3, -5, 5), (4, 8, -1), (4, 3), (3, -2, 7), (7, 6, 2), (2, 1), (1, 5, -4)]], 'tensors': [['tensor', 'T3_ket', 'C4', 'T4_bra', 'T4_ket', 'C1', 'T1_ket']]}

ctmrg_split_transfer_phys_left_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efUYV,beX,cb,cWd,dfZ->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor_conj', 'T4_bra', 'C4', 'T3_ket', 'T3_bra']], 'ncon_network': [(4, 5, -6, -2, -5), (1, 4, -3), (2, 1), (2, -4, 3), (3, 5, -1)], 'network': [[(4, 5, -6, -2, -5), (1, 4, -3), (2, 1), (2, -4, 3), (3, 5, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, -6, -2, -5), (1, 4, -3), (2, 1), (2, -4, 3), (3, 5, -1)]], 'tensors': [['tensor_conj', 'T4_bra', 'C4', 'T3_ket', 'T3_bra']]}

ctmrg_split_transfer_phys_left_full: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eqUgd,bdf,cb,hec,pVh,onXYq,mop,ilm,ji,jnk,fgW,Zkl->ZYXWVU', 'filter_additional_tensors': ['projector_top_right_phys', 'projector_bottom_right_phys'], 'filter_peps_tensors': [['tensor', 'T1_ket', 'C1', 'T4_ket', 'T4_bra'], ['tensor', 'T4_ket', 'T4_bra', 'C4', 'T3_ket']], 'ncon_network': [(4, 16, -6, 6, 3), (1, 3, 5), (2, 1), (7, 4, 2), (15, -5, 7), (14, 13, -3, -2, 16), (12, 14, 15), (8, 11, 12), (9, 8), (9, 13, 10), (5, 6, -4), (-1, 10, 11)], 'network': [[(4, 16, -6, 6, 3), (1, 3, 5), (2, 1), (7, 4, 2), (15, -5, 7)], [(14, 13, -3, -2, 16), (12, 14, 15), (8, 11, 12), (9, 8), (9, 13, 10)], (5, 6, -4), (-1, 10, 11)], 'network_additional_tensors': [(5, 6, -4), (-1, 10, 11)], 'network_peps_tensors': [[(4, 16, -6, 6, 3), (1, 3, 5), (2, 1), (7, 4, 2), (15, -5, 7)], [(14, 13, -3, -2, 16), (12, 14, 15), (8, 11, 12), (9, 8), (9, 13, 10)]], 'tensors': [['tensor', 'T1_ket', 'C1', 'T4_ket', 'T4_bra'], ['tensor', 'T4_ket', 'T4_bra', 'C4', 'T3_ket'], 'projector_top_right_phys', 'projector_bottom_right_phys']}

ctmrg_split_transfer_phys_left_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dYWUe,Zdb,bc,cef,fXV->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'T4_ket', 'C1', 'T1_ket', 'T1_bra']], 'ncon_network': [(3, -2, -4, -6, 4), (-1, 3, 1), (1, 2), (2, 4, 5), (5, -3, -5)], 'network': [[(3, -2, -4, -6, 4), (-1, 3, 1), (1, 2), (2, 4, 5), (5, -3, -5)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, -2, -4, -6, 4), (-1, 3, 1), (1, 2), (2, 4, 5), (5, -3, -5)]], 'tensors': [['tensor', 'T4_ket', 'C1', 'T1_ket', 'T1_bra']]}

ctmrg_split_transfer_phys_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WfVgi,Zie,ed,hYd,cgh,bc,Xfb->ZYXWV', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor_conj', 'T1_bra', 'C2', 'T2_ket', 'T2_bra', 'C3', 'T3_bra']], 'ncon_network': [(-4, 5, -5, 6, 8), (-1, 8, 4), (4, 3), (7, -2, 3), (2, 6, 7), (1, 2), (-3, 5, 1)], 'network': [[(-4, 5, -5, 6, 8), (-1, 8, 4), (4, 3), (7, -2, 3), (2, 6, 7), (1, 2), (-3, 5, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-4, 5, -5, 6, 8), (-1, 8, 4), (4, 3), (7, -2, 3), (2, 6, 7), (1, 2), (-3, 5, 1)]], 'tensors': [['tensor_conj', 'T1_bra', 'C2', 'T2_ket', 'T2_bra', 'C3', 'T3_bra']]}

ctmrg_split_transfer_phys_right_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'UeWdX,bdZ,cb,fec,VYf->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor_conj', 'T2_bra', 'C3', 'T3_bra', 'T3_ket']], 'ncon_network': [(-6, 4, -4, 3, -3), (1, 3, -1), (2, 1), (5, 4, 2), (-5, -2, 5)], 'network': [[(-6, 4, -4, 3, -3), (1, 3, -1), (2, 1), (5, 4, 2), (-5, -2, 5)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-6, 4, -4, 3, -3), (1, 3, -1), (2, 1), (5, 4, 2), (-5, -2, 5)]], 'tensors': [['tensor_conj', 'T2_bra', 'C3', 'T3_bra', 'T3_ket']]}

ctmrg_split_transfer_phys_right_full: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YqXon,knj,ji,mli,pom,gdUeq,hVp,ceh,bc,fdb,Zkl,fgW->ZYXWVU', 'filter_additional_tensors': ['projector_top_left_phys', 'projector_bottom_left_phys'], 'filter_peps_tensors': [['tensor_conj', 'T1_bra', 'C2', 'T2_ket', 'T2_bra'], ['tensor_conj', 'T2_ket', 'T2_bra', 'C3', 'T3_bra']], 'ncon_network': [(-2, 16, -3, 14, 13), (10, 13, 9), (9, 8), (12, 11, 8), (15, 14, 12), (6, 3, -6, 4, 16), (7, -5, 15), (2, 4, 7), (1, 2), (5, 3, 1), (-1, 10, 11), (5, 6, -4)], 'network': [[(-2, 16, -3, 14, 13), (10, 13, 9), (9, 8), (12, 11, 8), (15, 14, 12)], [(6, 3, -6, 4, 16), (7, -5, 15), (2, 4, 7), (1, 2), (5, 3, 1)], (-1, 10, 11), (5, 6, -4)], 'network_additional_tensors': [(-1, 10, 11), (5, 6, -4)], 'network_peps_tensors': [[(-2, 16, -3, 14, 13), (10, 13, 9), (9, 8), (12, 11, 8), (15, 14, 12)], [(6, 3, -6, 4, 16), (7, -5, 15), (2, 4, 7), (1, 2), (5, 3, 1)]], 'tensors': [['tensor_conj', 'T1_bra', 'C2', 'T2_ket', 'T2_bra'], ['tensor_conj', 'T2_ket', 'T2_bra', 'C3', 'T3_bra'], 'projector_top_left_phys', 'projector_bottom_left_phys']}

ctmrg_split_transfer_phys_right_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YWUef,Zfd,dVc,cb,Xeb->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'T1_ket', 'T1_bra', 'C2', 'T2_ket']], 'ncon_network': [(-2, -4, -6, 4, 5), (-1, 5, 3), (3, -5, 2), (2, 1), (-3, 4, 1)], 'network': [[(-2, -4, -6, 4, 5), (-1, 5, 3), (3, -5, 2), (2, 1), (-3, 4, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, -4, -6, 4, 5), (-1, 5, 3), (3, -5, 2), (2, 1), (-3, 4, 1)]], 'tensors': [['tensor', 'T1_ket', 'T1_bra', 'C2', 'T2_ket']]}

ctmrg_split_transfer_phys_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fYVig,Zfb,bc,cgh,hWd,de,Xie->ZYXWV', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'T4_ket', 'C1', 'T1_ket', 'T1_bra', 'C2', 'T2_ket']], 'ncon_network': [(5, -2, -5, 8, 6), (-1, 5, 1), (1, 2), (2, 6, 7), (7, -4, 3), (3, 4), (-3, 8, 4)], 'network': [[(5, -2, -5, 8, 6), (-1, 5, 1), (1, 2), (2, 6, 7), (7, -4, 3), (3, 4), (-3, 8, 4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, -2, -5, 8, 6), (-1, 5, 1), (1, 2), (2, 6, 7), (7, -4, 3), (3, 4), (-3, 8, 4)]], 'tensors': [['tensor', 'T4_ket', 'C1', 'T1_ket', 'T1_bra', 'C2', 'T2_ket']]}

ctmrg_split_transfer_phys_top_full: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dgXqe,fdb,bc,ceh,hYp,qVUno,pom,mli,ij,knj,Zfg,klW->ZYXWVU', 'filter_additional_tensors': ['projector_left_bottom_ket', 'projector_right_bottom_bra'], 'filter_peps_tensors': [['tensor', 'T4_ket', 'C1', 'T1_ket', 'T1_bra'], ['tensor', 'T1_ket', 'T1_bra', 'C2', 'T2_ket']], 'ncon_network': [(3, 6, -3, 16, 4), (5, 3, 1), (1, 2), (2, 4, 7), (7, -2, 15), (16, -5, -6, 13, 14), (15, 14, 12), (12, 11, 8), (8, 9), (10, 13, 9), (-1, 5, 6), (10, 11, -4)], 'network': [[(3, 6, -3, 16, 4), (5, 3, 1), (1, 2), (2, 4, 7), (7, -2, 15)], [(16, -5, -6, 13, 14), (15, 14, 12), (12, 11, 8), (8, 9), (10, 13, 9)], (-1, 5, 6), (10, 11, -4)], 'network_additional_tensors': [(-1, 5, 6), (10, 11, -4)], 'network_peps_tensors': [[(3, 6, -3, 16, 4), (5, 3, 1), (1, 2), (2, 4, 7), (7, -2, 15)], [(16, -5, -6, 13, 14), (15, 14, 12), (12, 11, 8), (8, 9), (10, 13, 9)]], 'tensors': [['tensor', 'T4_ket', 'C1', 'T1_ket', 'T1_bra'], ['tensor', 'T1_ket', 'T1_bra', 'C2', 'T2_ket'], 'projector_left_bottom_ket', 'projector_right_bottom_bra']}

ctmrg_split_transfer_phys_top_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eYUWd,ZVf,fec,cb,bdX->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'T4_bra', 'T4_ket', 'C1', 'T1_ket']], 'ncon_network': [(4, -2, -6, -4, 3), (-1, -5, 5), (5, 4, 2), (2, 1), (1, 3, -3)], 'network': [[(4, -2, -6, -4, 3), (-1, -5, 5), (5, 4, 2), (2, 1), (1, 3, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, -2, -6, -4, 3), (-1, -5, 5), (5, 4, 2), (2, 1), (1, 3, -3)]], 'tensors': [['tensor', 'T4_bra', 'T4_ket', 'C1', 'T1_ket']]}

ctmrg_split_transfer_phys_top_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'XUWfe,Zeb,bc,dYc,Vfd->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor_conj', 'T1_bra', 'C2', 'T2_ket', 'T2_bra']], 'ncon_network': [(-3, -6, -4, 5, 4), (-1, 4, 1), (1, 2), (3, -2, 2), (-5, 5, 3)], 'network': [[(-3, -6, -4, 5, 4), (-1, 4, 1), (1, 2), (3, -2, 2), (-5, 5, 3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-3, -6, -4, 5, 4), (-1, 4, 1), (1, 2), (3, -2, 2), (-5, 5, 3)]], 'tensors': [['tensor_conj', 'T1_bra', 'C2', 'T2_ket', 'T2_bra']]}

ctmrg_split_transfer_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Ykmlo,Wfmgi,Zon,nib,bc,hlc,dgh,ed,jfe,Xkj->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra', 'C3', 'T3_bra', 'T3_ket']], 'ncon_network': [(-2, 10, 12, 11, 14), (-4, 5, 12, 6, 8), (-1, 14, 13), (13, 8, 1), (1, 2), (7, 11, 2), (3, 6, 7), (4, 3), (9, 5, 4), (-3, 10, 9)], 'network': [[(-2, 10, 12, 11, 14), (-4, 5, 12, 6, 8), (-1, 14, 13), (13, 8, 1), (1, 2), (7, 11, 2), (3, 6, 7), (4, 3), (9, 5, 4), (-3, 10, 9)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 10, 12, 11, 14), (-4, 5, 12, 6, 8), (-1, 14, 13), (13, 8, 1), (1, 2), (7, 11, 2), (3, 6, 7), (4, 3), (9, 5, 4), (-3, 10, 9)]], 'tensors': [['tensor', 'tensor_conj', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra', 'C3', 'T3_bra', 'T3_ket']]}

ctmrg_split_transfer_right_bottom_half: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WlnmY,ifngk,blh,hfc,cd,dgj,jme,biX,Zek->ZYXW', 'filter_additional_tensors': ['projector_bottom_right_bra', 'projector_right_top_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3_ket', 'T3_bra', 'C3', 'T2_bra', 'T2_ket']], 'ncon_network': [(-4, 11, 13, 12, -2), (8, 5, 13, 6, 10), (1, 11, 7), (7, 5, 2), (2, 3), (3, 6, 9), (9, 12, 4), (1, 8, -3), (-1, 4, 10)], 'network': [[(-4, 11, 13, 12, -2), (8, 5, 13, 6, 10), (1, 11, 7), (7, 5, 2), (2, 3), (3, 6, 9), (9, 12, 4)], (1, 8, -3), (-1, 4, 10)], 'network_additional_tensors': [(1, 8, -3), (-1, 4, 10)], 'network_peps_tensors': [[(-4, 11, 13, 12, -2), (8, 5, 13, 6, 10), (1, 11, 7), (7, 5, 2), (2, 3), (3, 6, 9), (9, 12, 4)]], 'tensors': [['tensor', 'tensor_conj', 'T3_ket', 'T3_bra', 'C3', 'T2_bra', 'T2_ket'], 'projector_bottom_right_bra', 'projector_right_top_bra']}

ctmrg_split_transfer_right_full: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'pzusq,Yyuwv,oqr,rvm,mn,tsn,xwt,Wjklz,hfkey,ilx,cei,dc,gfd,bjg,Zop,bhX->ZYXW', 'filter_additional_tensors': ['projector_top_left_ket', 'projector_bottom_left_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra'], ['tensor', 'tensor_conj', 'T2_ket', 'T2_bra', 'C3', 'T3_bra', 'T3_ket']], 'ncon_network': [(15, 25, 20, 18, 16), (-2, 24, 20, 22, 21), (14, 16, 17), (17, 21, 12), (12, 13), (19, 18, 13), (23, 22, 19), (-4, 9, 10, 11, 25), (7, 5, 10, 4, 24), (8, 11, 23), (2, 4, 8), (3, 2), (6, 5, 3), (1, 9, 6), (-1, 14, 15), (1, 7, -3)], 'network': [[(15, 25, 20, 18, 16), (-2, 24, 20, 22, 21), (14, 16, 17), (17, 21, 12), (12, 13), (19, 18, 13), (23, 22, 19)], [(-4, 9, 10, 11, 25), (7, 5, 10, 4, 24), (8, 11, 23), (2, 4, 8), (3, 2), (6, 5, 3), (1, 9, 6)], (-1, 14, 15), (1, 7, -3)], 'network_additional_tensors': [(-1, 14, 15), (1, 7, -3)], 'network_peps_tensors': [[(15, 25, 20, 18, 16), (-2, 24, 20, 22, 21), (14, 16, 17), (17, 21, 12), (12, 13), (19, 18, 13), (23, 22, 19)], [(-4, 9, 10, 11, 25), (7, 5, 10, 4, 24), (8, 11, 23), (2, 4, 8), (3, 2), (6, 5, 3), (1, 9, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra'], ['tensor', 'tensor_conj', 'T2_ket', 'T2_bra', 'C3', 'T3_bra', 'T3_ket'], 'projector_top_left_ket', 'projector_bottom_left_bra']}

ctmrg_split_transfer_right_top_half: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fWnig,Yknjm,bgh,hmc,cd,lid,ejl,Zbf,ekX->ZYXW', 'filter_additional_tensors': ['projector_top_left_ket', 'projector_right_bottom_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra']], 'ncon_network': [(5, -4, 13, 8, 6), (-2, 10, 13, 9, 12), (1, 6, 7), (7, 12, 2), (2, 3), (11, 8, 3), (4, 9, 11), (-1, 1, 5), (4, 10, -3)], 'network': [[(5, -4, 13, 8, 6), (-2, 10, 13, 9, 12), (1, 6, 7), (7, 12, 2), (2, 3), (11, 8, 3), (4, 9, 11)], (-1, 1, 5), (4, 10, -3)], 'network_additional_tensors': [(-1, 1, 5), (4, 10, -3)], 'network_peps_tensors': [[(5, -4, 13, 8, 6), (-2, 10, 13, 9, 12), (1, 6, 7), (7, 12, 2), (2, 3), (11, 8, 3), (4, 9, 11)]], 'tensors': [['tensor', 'tensor_conj', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra'], 'projector_top_left_ket', 'projector_right_bottom_bra']}

ctmrg_split_transfer_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'gYmif,kWmol,Zkj,jgb,bc,cfh,hld,de,nie,Xon->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4_bra', 'T4_ket', 'C1', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra']], 'ncon_network': [(6, -2, 12, 8, 5), (10, -4, 12, 14, 11), (-1, 10, 9), (9, 6, 1), (1, 2), (2, 5, 7), (7, 11, 3), (3, 4), (13, 8, 4), (-3, 14, 13)], 'network': [[(6, -2, 12, 8, 5), (10, -4, 12, 14, 11), (-1, 10, 9), (9, 6, 1), (1, 2), (2, 5, 7), (7, 11, 3), (3, 4), (13, 8, 4), (-3, 14, 13)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, -2, 12, 8, 5), (10, -4, 12, 14, 11), (-1, 10, 9), (9, 6, 1), (1, 2), (2, 5, 7), (7, 11, 3), (3, 4), (13, 8, 4), (-3, 14, 13)]], 'tensors': [['tensor', 'tensor_conj', 'T4_bra', 'T4_ket', 'C1', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra']]}

ctmrg_split_transfer_top_full: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ehkxf,jYkyl,bjg,ged,dc,cfi,ilz,xWuvw,ypuqs,zwt,tsn,nm,rvm,oqr,Zbh,opX->ZYXW', 'filter_additional_tensors': ['projector_left_bottom_ket', 'projector_right_bottom_bra'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4_bra', 'T4_ket', 'C1', 'T1_ket', 'T1_bra'], ['tensor', 'tensor_conj', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra']], 'ncon_network': [(4, 7, 10, 23, 5), (9, -2, 10, 24, 11), (1, 9, 6), (6, 4, 3), (3, 2), (2, 5, 8), (8, 11, 25), (23, -4, 20, 21, 22), (24, 15, 20, 16, 18), (25, 22, 19), (19, 18, 13), (13, 12), (17, 21, 12), (14, 16, 17), (-1, 1, 7), (14, 15, -3)], 'network': [[(4, 7, 10, 23, 5), (9, -2, 10, 24, 11), (1, 9, 6), (6, 4, 3), (3, 2), (2, 5, 8), (8, 11, 25)], [(23, -4, 20, 21, 22), (24, 15, 20, 16, 18), (25, 22, 19), (19, 18, 13), (13, 12), (17, 21, 12), (14, 16, 17)], (-1, 1, 7), (14, 15, -3)], 'network_additional_tensors': [(-1, 1, 7), (14, 15, -3)], 'network_peps_tensors': [[(4, 7, 10, 23, 5), (9, -2, 10, 24, 11), (1, 9, 6), (6, 4, 3), (3, 2), (2, 5, 8), (8, 11, 25)], [(23, -4, 20, 21, 22), (24, 15, 20, 16, 18), (25, 22, 19), (19, 18, 13), (13, 12), (17, 21, 12), (14, 16, 17)]], 'tensors': [['tensor', 'tensor_conj', 'T4_bra', 'T4_ket', 'C1', 'T1_ket', 'T1_bra'], ['tensor', 'tensor_conj', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra'], 'projector_left_bottom_ket', 'projector_right_bottom_bra']}

ctmrg_top_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dYhVe,fXhUg,Zfdb,bc,cegW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4', 'C1', 'T1']], 'ncon_network': [(3, -2, 7, -5, 4), (5, -3, 7, -6, 6), (-1, 5, 3, 1), (1, 2), (2, 4, 6, -4)], 'network': [[(3, -2, 7, -5, 4), (5, -3, 7, -6, 6), (-1, 5, 3, 1), (1, 2), (2, 4, 6, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, -2, 7, -5, 4), (5, -3, 7, -6, 6), (-1, 5, 3, 1), (1, 2), (2, 4, 6, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T4', 'C1', 'T1']]}

Fig. 36 Contraction for top left CTM corner.

ctmrg_top_left_large_d = {'einsum_network': 'eYdVf,gXdUh,Zgeb,bc,cfhW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4', 'C1', 'T1']], 'ncon_network': [(4, -2, 3, -5, 5), (6, -3, 3, -6, 7), (-1, 6, 4, 1), (1, 2), (2, 5, 7, -4)], 'network': [[(4, -2, 3, -5, 5), (6, -3, 3, -6, 7), (-1, 6, 4, 1), (1, 2), (2, 5, 7, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, -2, 3, -5, 5), (6, -3, 3, -6, 7), (-1, 6, 4, 1), (1, 2), (2, 5, 7, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T4', 'C1', 'T1']]}

Fig. 37 Contraction for top left CTM corner for high physical dimensions.

ctmrg_top_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YUhed,XVhgf,Zdfb,bc,egWc->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2']], 'ncon_network': [(-2, -6, 7, 4, 3), (-3, -5, 7, 6, 5), (-1, 3, 5, 1), (1, 2), (4, 6, -4, 2)], 'network': [[(-2, -6, 7, 4, 3), (-3, -5, 7, 6, 5), (-1, 3, 5, 1), (1, 2), (4, 6, -4, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, -6, 7, 4, 3), (-3, -5, 7, 6, 5), (-1, 3, 5, 1), (1, 2), (4, 6, -4, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2']]}

Fig. 38 Contraction for top right CTM corner.

ctmrg_top_right_large_d: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YUdfe,XVdhg,Zegb,bc,fhWc->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2']], 'ncon_network': [(-2, -6, 3, 5, 4), (-3, -5, 3, 7, 6), (-1, 4, 6, 1), (1, 2), (5, 7, -4, 2)], 'network': [[(-2, -6, 3, 5, 4), (-3, -5, 3, 7, 6), (-1, 4, 6, 1), (1, 2), (5, 7, -4, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, -6, 3, 5, 4), (-3, -5, 3, 7, 6), (-1, 4, 6, 1), (1, 2), (5, 7, -4, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2']]}

Fig. 39 Contraction for top right CTM corner for high physical dimensions.

density_matrix_four_sites_bottom_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'deZVT,fgYWS,cXge,cb,bfdU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3', 'C4', 'T4']], 'ncon_network': [(3, 4, -1, -5, -7), (5, 6, -2, -4, -8), (2, -3, 6, 4), (2, 1), (1, 5, 3, -6)], 'network': [[(3, 4, -1, -5, -7), (5, 6, -2, -4, -8), (2, -3, 6, 4), (2, 1), (1, 5, 3, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, -1, -5, -7), (5, 6, -2, -4, -8), (2, -3, 6, 4), (2, 1), (1, 5, 3, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T3', 'C4', 'T4']]}

density_matrix_four_sites_bottom_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'SdZeV,TfYgW,egcX,Ubfd,bc->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2', 'T3', 'C3']], 'ncon_network': [(-8, 3, -1, 4, -5), (-7, 5, -2, 6, -4), (4, 6, 2, -3), (-6, 1, 5, 3), (1, 2)], 'network': [[(-8, 3, -1, 4, -5), (-7, 5, -2, 6, -4), (4, 6, 2, -3), (-6, 1, 5, 3), (1, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-8, 3, -1, 4, -5), (-7, 5, -2, 6, -4), (4, 6, 2, -3), (-6, 1, 5, 3), (1, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T2', 'T3', 'C3']]}

density_matrix_four_sites_top_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dWZTe,fVYSg,Xfdb,bc,cegU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4', 'C1', 'T1']], 'ncon_network': [(3, -4, -1, -7, 4), (5, -5, -2, -8, 6), (-3, 5, 3, 1), (1, 2), (2, 4, 6, -6)], 'network': [[(3, -4, -1, -7, 4), (5, -5, -2, -8, 6), (-3, 5, 3, 1), (1, 2), (2, 4, 6, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, -4, -1, -7, 4), (5, -5, -2, -8, 6), (-3, 5, 3, 1), (1, 2), (2, 4, 6, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T4', 'C1', 'T1']]}

density_matrix_four_sites_top_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WSZed,VTYgf,Xdfb,bc,egUc->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2']], 'ncon_network': [(-4, -8, -1, 4, 3), (-5, -7, -2, 6, 5), (-3, 3, 5, 1), (1, 2), (4, 6, -6, 2)], 'network': [[(-4, -8, -1, 4, 3), (-5, -7, -2, 6, 5), (-3, 3, 5, 1), (1, 2), (4, 6, -6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-4, -8, -1, 4, 3), (-5, -7, -2, 6, 5), (-3, 3, 5, 1), (1, 2), (4, 6, -6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2']]}

density_matrix_one_site: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4']]}

density_matrix_one_site_C1_phase: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1_phase', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1_phase', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4']]}

density_matrix_one_site_C2_phase: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2_phase', 'T2', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2_phase', 'T2', 'C3', 'T3', 'C4', 'T4']]}

density_matrix_one_site_C3_phase: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3_phase', 'T3', 'C4', 'T4']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3_phase', 'T3', 'C4', 'T4']]}

density_matrix_one_site_C4_phase: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4_phase', 'T4']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4_phase', 'T4']]}

density_matrix_one_site_T1_phase: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1_phase', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1_phase', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4']]}

density_matrix_one_site_T2_phase: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2_phase', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2_phase', 'C3', 'T3', 'C4', 'T4']]}

density_matrix_one_site_T3_phase: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3', 'T3_phase', 'C4', 'T4']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3', 'T3_phase', 'C4', 'T4']]}

density_matrix_one_site_T4_phase: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ghZkj,noYpq,cm,mjqd,di,kpei,le,bloh,bf,fngc->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4_phase']], 'ncon_network': [(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)], 'network': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(6, 7, -1, 10, 9), (13, 14, -2, 15, 16), (2, 12), (12, 9, 16, 3), (3, 8), (10, 15, 4, 8), (11, 4), (1, 11, 14, 7), (1, 5), (5, 13, 6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4_phase']]}

density_matrix_three_sites_triangle_without_top_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'klmbcd,ZWbcdefg,YVhijklm,XUefghij->ZYXWVU', 'filter_additional_tensors': ['top-left', 'top-right', 'bottom-left', 'bottom-right'], 'filter_peps_tensors': [], 'ncon_network': [(10, 11, 12, 1, 2, 3), (-1, -4, 1, 2, 3, 4, 5, 6), (-2, -5, 7, 8, 9, 10, 11, 12), (-3, -6, 4, 5, 6, 7, 8, 9)], 'network': [(10, 11, 12, 1, 2, 3), (-1, -4, 1, 2, 3, 4, 5, 6), (-2, -5, 7, 8, 9, 10, 11, 12), (-3, -6, 4, 5, 6, 7, 8, 9)], 'network_additional_tensors': [(10, 11, 12, 1, 2, 3), (-1, -4, 1, 2, 3, 4, 5, 6), (-2, -5, 7, 8, 9, 10, 11, 12), (-3, -6, 4, 5, 6, 7, 8, 9)], 'network_peps_tensors': [], 'tensors': ['top-left', 'top-right', 'bottom-left', 'bottom-right']}

density_matrix_two_sites_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efViY,ghUjX,ijcW,kc,bkhf,bd,dgeZ->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(4, 5, -5, 8, -2), (6, 7, -6, 9, -3), (8, 9, 2, -4), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -1)], 'network': [[(4, 5, -5, 8, -2), (6, 7, -6, 9, -3), (8, 9, 2, -4), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, -5, 8, -2), (6, 7, -6, 9, -3), (8, 9, 2, -4), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T2', 'C3', 'T3', 'C4', 'T4']]}

density_matrix_two_sites_horizontal_rectangle: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fljtg,hnjui,egis,kqozl,mroAn,pyrq,ZXbcdefh,stuvwx,pmkbcd,YWvwxyAz->ZYXW', 'filter_additional_tensors': ['top_left', 'top_right', 'bottom_left', 'bottom_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1'], ['tensor', 'tensor_conj', 'T3']], 'ncon_network': [(5, 11, 9, 19, 6), (7, 13, 9, 20, 8), (4, 6, 8, 18), (10, 16, 14, 25, 11), (12, 17, 14, 26, 13), (15, 24, 17, 16), (-1, -3, 1, 2, 3, 4, 5, 7), (18, 19, 20, 21, 22, 23), (15, 12, 10, 1, 2, 3), (-2, -4, 21, 22, 23, 24, 26, 25)], 'network': [[(5, 11, 9, 19, 6), (7, 13, 9, 20, 8), (4, 6, 8, 18)], [(10, 16, 14, 25, 11), (12, 17, 14, 26, 13), (15, 24, 17, 16)], (-1, -3, 1, 2, 3, 4, 5, 7), (18, 19, 20, 21, 22, 23), (15, 12, 10, 1, 2, 3), (-2, -4, 21, 22, 23, 24, 26, 25)], 'network_additional_tensors': [(-1, -3, 1, 2, 3, 4, 5, 7), (18, 19, 20, 21, 22, 23), (15, 12, 10, 1, 2, 3), (-2, -4, 21, 22, 23, 24, 26, 25)], 'network_peps_tensors': [[(5, 11, 9, 19, 6), (7, 13, 9, 20, 8), (4, 6, 8, 18)], [(10, 16, 14, 25, 11), (12, 17, 14, 26, 13), (15, 24, 17, 16)]], 'tensors': [['tensor', 'tensor_conj', 'T1'], ['tensor', 'tensor_conj', 'T3'], 'top_left', 'top_right', 'bottom_left', 'bottom_right']}

density_matrix_two_sites_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fjZWe,hkYVg,bd,degX,cUkj,ci,ihfb->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'T3', 'C4', 'T4']], 'ncon_network': [(5, 9, -1, -4, 4), (7, 10, -2, -5, 6), (1, 3), (3, 4, 6, -3), (2, -6, 10, 9), (2, 8), (8, 7, 5, 1)], 'network': [[(5, 9, -1, -4, 4), (7, 10, -2, -5, 6), (1, 3), (3, 4, 6, -3), (2, -6, 10, 9), (2, 8), (8, 7, 5, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 9, -1, -4, 4), (7, 10, -2, -5, 6), (1, 3), (3, 4, 6, -3), (2, -6, 10, 9), (2, 8), (8, 7, 5, 1)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'T3', 'C4', 'T4']]}

density_matrix_two_sites_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YiVfe,XjUhg,Zegd,db,fhkb,Wcji,ck->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2', 'T3', 'C3']], 'ncon_network': [(-2, 8, -5, 5, 4), (-3, 9, -6, 7, 6), (-1, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-4, 2, 9, 8), (2, 10)], 'network': [[(-2, 8, -5, 5, 4), (-3, 9, -6, 7, 6), (-1, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-4, 2, 9, 8), (2, 10)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 8, -5, 5, 4), (-3, 9, -6, 7, 6), (-1, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-4, 2, 9, 8), (2, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2', 'T3', 'C3']]}

density_matrix_two_sites_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'iWZef,jVYgh,ck,kfhb,bd,egUd,Xjic->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'T4']], 'ncon_network': [(8, -4, -1, 4, 5), (9, -5, -2, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -6, 3), (-3, 9, 8, 2)], 'network': [[(8, -4, -1, 4, 5), (9, -5, -2, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -6, 3), (-3, 9, 8, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(8, -4, -1, 4, 5), (9, -5, -2, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -6, 3), (-3, 9, 8, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'T4']]}

density_matrix_two_sites_vertical_rectangle: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'gtjlf,iujnh,sige,lwoqk,nxorm,qrvp,ZXefhbcd,bcdpmk,yzAstu,YWvxwyzA->ZYXW', 'filter_additional_tensors': ['top_left', 'top_right', 'bottom_left', 'bottom_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4'], ['tensor', 'tensor_conj', 'T2']], 'ncon_network': [(6, 19, 9, 11, 5), (8, 20, 9, 13, 7), (18, 8, 6, 4), (11, 22, 14, 16, 10), (13, 23, 14, 17, 12), (16, 17, 21, 15), (-1, -3, 4, 5, 7, 1, 2, 3), (1, 2, 3, 15, 12, 10), (24, 25, 26, 18, 19, 20), (-2, -4, 21, 23, 22, 24, 25, 26)], 'network': [[(6, 19, 9, 11, 5), (8, 20, 9, 13, 7), (18, 8, 6, 4)], [(11, 22, 14, 16, 10), (13, 23, 14, 17, 12), (16, 17, 21, 15)], (-1, -3, 4, 5, 7, 1, 2, 3), (1, 2, 3, 15, 12, 10), (24, 25, 26, 18, 19, 20), (-2, -4, 21, 23, 22, 24, 25, 26)], 'network_additional_tensors': [(-1, -3, 4, 5, 7, 1, 2, 3), (1, 2, 3, 15, 12, 10), (24, 25, 26, 18, 19, 20), (-2, -4, 21, 23, 22, 24, 25, 26)], 'network_peps_tensors': [[(6, 19, 9, 11, 5), (8, 20, 9, 13, 7), (18, 8, 6, 4)], [(11, 22, 14, 16, 10), (13, 23, 14, 17, 12), (16, 17, 21, 15)]], 'tensors': [['tensor', 'tensor_conj', 'T4'], ['tensor', 'tensor_conj', 'T2'], 'top_left', 'top_right', 'bottom_left', 'bottom_right']}

honeycomb_density_matrix_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eflViY,ghlUjX,ijcW,kc,bkhf,bd,dgeZ->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(4, 5, 11, -5, 8, -2), (6, 7, 11, -6, 9, -3), (8, 9, 2, -4), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -1)], 'network': [[(4, 5, 11, -5, 8, -2), (6, 7, 11, -6, 9, -3), (8, 9, 2, -4), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, 11, -5, 8, -2), (6, 7, 11, -6, 9, -3), (8, 9, 2, -4), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T2', 'C3', 'T3', 'C4', 'T4']]}

honeycomb_density_matrix_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fjlZWe,hklYVg,bd,degX,cUkj,ci,ihfb->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'T3', 'C4', 'T4']], 'ncon_network': [(5, 9, 11, -1, -4, 4), (7, 10, 11, -2, -5, 6), (1, 3), (3, 4, 6, -3), (2, -6, 10, 9), (2, 8), (8, 7, 5, 1)], 'network': [[(5, 9, 11, -1, -4, 4), (7, 10, 11, -2, -5, 6), (1, 3), (3, 4, 6, -3), (2, -6, 10, 9), (2, 8), (8, 7, 5, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 9, 11, -1, -4, 4), (7, 10, 11, -2, -5, 6), (1, 3), (3, 4, 6, -3), (2, -6, 10, 9), (2, 8), (8, 7, 5, 1)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'T3', 'C4', 'T4']]}

honeycomb_density_matrix_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YiVlfe,XjUlhg,Zegd,db,fhkb,Wcji,ck->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2', 'T3', 'C3']], 'ncon_network': [(-2, 8, -5, 11, 5, 4), (-3, 9, -6, 11, 7, 6), (-1, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-4, 2, 9, 8), (2, 10)], 'network': [[(-2, 8, -5, 11, 5, 4), (-3, 9, -6, 11, 7, 6), (-1, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-4, 2, 9, 8), (2, 10)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 8, -5, 11, 5, 4), (-3, 9, -6, 11, 7, 6), (-1, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-4, 2, 9, 8), (2, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2', 'T3', 'C3']]}

honeycomb_density_matrix_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'iWZlef,jVYlgh,ck,kfhb,bd,egUd,Xjic->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'T4']], 'ncon_network': [(8, -4, -1, 11, 4, 5), (9, -5, -2, 11, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -6, 3), (-3, 9, 8, 2)], 'network': [[(8, -4, -1, 11, 4, 5), (9, -5, -2, 11, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -6, 3), (-3, 9, 8, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(8, -4, -1, 11, 4, 5), (9, -5, -2, 11, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -6, 3), (-3, 9, 8, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'T4']]}

classmethod join_defs(name1, name2, join_indices)

kagome_downward_triangle_bottom_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dehiZVT,fghiYWS,cXge,cb,bfdU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3', 'C4', 'T4']], 'ncon_network': [(3, 4, 7, 8, -1, -5, -7), (5, 6, 7, 8, -2, -4, -8), (2, -3, 6, 4), (2, 1), (1, 5, 3, -6)], 'network': [[(3, 4, 7, 8, -1, -5, -7), (5, 6, 7, 8, -2, -4, -8), (2, -3, 6, 4), (2, 1), (1, 5, 3, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 7, 8, -1, -5, -7), (5, 6, 7, 8, -2, -4, -8), (2, -3, 6, 4), (2, 1), (1, 5, 3, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T3', 'C4', 'T4']]}

kagome_downward_triangle_bottom_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'SdZhieV,TfYhigW,egcX,Ubfd,bc->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2', 'T3', 'C3']], 'ncon_network': [(-8, 3, -1, 7, 8, 4, -5), (-7, 5, -2, 7, 8, 6, -4), (4, 6, 2, -3), (-6, 1, 5, 3), (1, 2)], 'network': [[(-8, 3, -1, 7, 8, 4, -5), (-7, 5, -2, 7, 8, 6, -4), (4, 6, 2, -3), (-6, 1, 5, 3), (1, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-8, 3, -1, 7, 8, 4, -5), (-7, 5, -2, 7, 8, 6, -4), (4, 6, 2, -3), (-6, 1, 5, 3), (1, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T2', 'T3', 'C3']]}

kagome_downward_triangle_top_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dWhiZTe,fVhiYSg,Xfdb,bc,cegU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4', 'C1', 'T1']], 'ncon_network': [(3, -4, 7, 8, -1, -7, 4), (5, -5, 7, 8, -2, -8, 6), (-3, 5, 3, 1), (1, 2), (2, 4, 6, -6)], 'network': [[(3, -4, 7, 8, -1, -7, 4), (5, -5, 7, 8, -2, -8, 6), (-3, 5, 3, 1), (1, 2), (2, 4, 6, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, -4, 7, 8, -1, -7, 4), (5, -5, 7, 8, -2, -8, 6), (-3, 5, 3, 1), (1, 2), (2, 4, 6, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T4', 'C1', 'T1']]}

kagome_downward_triangle_top_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WShZied,VThYigf,Xdfb,bc,egUc->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2']], 'ncon_network': [(-4, -8, 7, -1, 8, 4, 3), (-5, -7, 7, -2, 8, 6, 5), (-3, 3, 5, 1), (1, 2), (4, 6, -6, 2)], 'network': [[(-4, -8, 7, -1, 8, 4, 3), (-5, -7, 7, -2, 8, 6, 5), (-3, 3, 5, 1), (1, 2), (4, 6, -6, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-4, -8, 7, -1, 8, 4, 3), (-5, -7, 7, -2, 8, 6, 5), (-3, 3, 5, 1), (1, 2), (4, 6, -6, 2)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2']]}

kagome_pess3_single_site_mapping: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bcd,ZTe,eXb,YWc,UVd->ZYXWVUT', 'filter_additional_tensors': ['up_simplex', 'down_simplex', 'site1', 'site2', 'site3'], 'filter_peps_tensors': [], 'ncon_network': [(1, 2, 3), (-1, -7, 4), (4, -3, 1), (-2, -4, 2), (-6, -5, 3)], 'network': [(1, 2, 3), (-1, -7, 4), (4, -3, 1), (-2, -4, 2), (-6, -5, 3)], 'network_additional_tensors': [(1, 2, 3), (-1, -7, 4), (4, -3, 1), (-2, -4, 2), (-6, -5, 3)], 'network_peps_tensors': [], 'tensors': ['up_simplex', 'down_simplex', 'site1', 'site2', 'site3']}

kagome_pess_mapping_upper_triangle: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bcd,ZeY,TXb,eWc,UVd->ZYXWVUT', 'filter_additional_tensors': ['up', 'down', 'site_1', 'site_2', 'site_3'], 'filter_peps_tensors': [], 'ncon_network': [[1, 2, 3], [-1, 4, -2], [-7, -3, 1], [4, -4, 2], [-6, -5, 3]], 'network': [[1, 2, 3], [-1, 4, -2], [-7, -3, 1], [4, -4, 2], [-6, -5, 3]], 'network_additional_tensors': [[1, 2, 3], [-1, 4, -2], [-7, -3, 1], [4, -4, 2], [-6, -5, 3]], 'network_peps_tensors': [], 'tensors': ['up', 'down', 'site_1', 'site_2', 'site_3']}

maple_leaf_pess_mapping: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'XZb,WYc,Ved,bce,dTU->ZYXWVUT', 'filter_additional_tensors': ['t1', 't2', 't3', 'up', 'down'], 'filter_peps_tensors': [], 'ncon_network': [(-3, -1, 1), (-4, -2, 2), (-5, 4, 3), (1, 2, 4), (3, -7, -6)], 'network': [(-3, -1, 1), (-4, -2, 2), (-5, 4, 3), (1, 2, 4), (3, -7, -6)], 'network_additional_tensors': [(-3, -1, 1), (-4, -2, 2), (-5, 4, 3), (1, 2, 4), (3, -7, -6)], 'network_peps_tensors': [], 'tensors': ['t1', 't2', 't3', 'up', 'down']}

overlap_four_sites_square_only_corners: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,cd,ed,eb->', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C1'], ['C2'], ['C3'], ['C4']], 'ncon_network': [(1, 2), (2, 3), (4, 3), (4, 1)], 'network': [[(1, 2)], [(2, 3)], [(4, 3)], [(4, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(1, 2)], [(2, 3)], [(4, 3)], [(4, 1)]], 'tensors': [['C1'], ['C2'], ['C3'], ['C4']]}

overlap_four_sites_square_transfer_horizontal: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,cefl,ljkh,hg,ig,mikj,dmfe,db->', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C1', 'T1'], ['T1', 'C2'], ['C3', 'T3'], ['T3', 'C4']], 'ncon_network': [(1, 2), (2, 4, 5, 11), (11, 9, 10, 7), (7, 6), (8, 6), (12, 8, 10, 9), (3, 12, 5, 4), (3, 1)], 'network': [[(1, 2), (2, 4, 5, 11)], [(11, 9, 10, 7), (7, 6)], [(8, 6), (12, 8, 10, 9)], [(3, 12, 5, 4), (3, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(1, 2), (2, 4, 5, 11)], [(11, 9, 10, 7), (7, 6)], [(8, 6), (12, 8, 10, 9)], [(3, 12, 5, 4), (3, 1)]], 'tensors': [['C1', 'T1'], ['T1', 'C2'], ['C3', 'T3'], ['T3', 'C4']]}

overlap_four_sites_square_transfer_vertical: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'lfec,cb,bd,efmd,jkhm,gh,gi,ikjl->', 'filter_additional_tensors': [], 'filter_peps_tensors': [['T4', 'C1'], ['C2', 'T2'], ['T2', 'C3'], ['C4', 'T4']], 'ncon_network': [(11, 5, 4, 2), (2, 1), (1, 3), (4, 5, 12, 3), (9, 10, 7, 12), (6, 7), (6, 8), (8, 10, 9, 11)], 'network': [[(11, 5, 4, 2), (2, 1)], [(1, 3), (4, 5, 12, 3)], [(9, 10, 7, 12), (6, 7)], [(6, 8), (8, 10, 9, 11)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(11, 5, 4, 2), (2, 1)], [(1, 3), (4, 5, 12, 3)], [(9, 10, 7, 12), (6, 7)], [(6, 8), (8, 10, 9, 11)]], 'tensors': [['T4', 'C1'], ['C2', 'T2'], ['T2', 'C3'], ['C4', 'T4']]}

overlap_one_site_only_corners: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,cd,ed,eb->', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C1', 'C2', 'C3', 'C4']], 'ncon_network': [(1, 2), (2, 3), (4, 3), (4, 1)], 'network': [[(1, 2), (2, 3), (4, 3), (4, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(1, 2), (2, 3), (4, 3), (4, 1)]], 'tensors': [['C1', 'C2', 'C3', 'C4']]}

overlap_one_site_only_transfer_horizontal: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,cefg,gh,hi,dife,db->', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C1', 'T1', 'C2', 'C3', 'T3', 'C4']], 'ncon_network': [(1, 2), (2, 4, 5, 6), (6, 7), (7, 8), (3, 8, 5, 4), (3, 1)], 'network': [[(1, 2), (2, 4, 5, 6), (6, 7), (7, 8), (3, 8, 5, 4), (3, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(1, 2), (2, 4, 5, 6), (6, 7), (7, 8), (3, 8, 5, 4), (3, 1)]], 'tensors': [['C1', 'T1', 'C2', 'C3', 'T3', 'C4']]}

overlap_one_site_only_transfer_vertical: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cb,bd,efid,hi,hg,gfec->', 'filter_additional_tensors': [], 'filter_peps_tensors': [['C1', 'C2', 'T2', 'C3', 'C4', 'T4']], 'ncon_network': [(2, 1), (1, 3), (4, 5, 8, 3), (7, 8), (7, 6), (6, 5, 4, 2)], 'network': [[(2, 1), (1, 3), (4, 5, 8, 3), (7, 8), (7, 6), (6, 5, 4, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(2, 1), (1, 3), (4, 5, 8, 3), (7, 8), (7, 6), (6, 5, 4, 2)]], 'tensors': [['C1', 'C2', 'T2', 'C3', 'C4', 'T4']]}

precondition_operator: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'cm,mjVd,di,kWei,le,blYh,bf,fZgc,ghXkj->ZYXWV', 'filter_additional_tensors': ['ket_tensor'], 'filter_peps_tensors': [['C1', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(2, 12), (12, 9, -5, 3), (3, 8), (10, -4, 4, 8), (11, 4), (1, 11, -2, 7), (1, 5), (5, -1, 6, 2), (6, 7, -3, 10, 9)], 'network': [[(2, 12), (12, 9, -5, 3), (3, 8), (10, -4, 4, 8), (11, 4), (1, 11, -2, 7), (1, 5), (5, -1, 6, 2)], (6, 7, -3, 10, 9)], 'network_additional_tensors': [(6, 7, -3, 10, 9)], 'network_peps_tensors': [[(2, 12), (12, 9, -5, 3), (3, 8), (10, -4, 4, 8), (11, 4), (1, 11, -2, 7), (1, 5), (5, -1, 6, 2)]], 'tensors': [['C1', 'T1', 'C2', 'T2', 'C3', 'T3', 'C4', 'T4'], 'ket_tensor']}

precondition_operator_split_transfer: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'bc,cnd,dVe,ef,gof,hWg,ih,jpi,kYj,kl,lqm,mZb,qpXon->ZYXWV', 'filter_additional_tensors': ['ket_tensor'], 'filter_peps_tensors': [['C1', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra', 'C3', 'T3_bra', 'T3_ket', 'C4', 'T4_bra', 'T4_ket']], 'ncon_network': [(1, 2), (2, 13, 3), (3, -5, 4), (4, 5), (6, 14, 5), (7, -4, 6), (8, 7), (9, 15, 8), (10, -2, 9), (10, 11), (11, 16, 12), (12, -1, 1), (16, 15, -3, 14, 13)], 'network': [[(1, 2), (2, 13, 3), (3, -5, 4), (4, 5), (6, 14, 5), (7, -4, 6), (8, 7), (9, 15, 8), (10, -2, 9), (10, 11), (11, 16, 12), (12, -1, 1)], (16, 15, -3, 14, 13)], 'network_additional_tensors': [(16, 15, -3, 14, 13)], 'network_peps_tensors': [[(1, 2), (2, 13, 3), (3, -5, 4), (4, 5), (6, 14, 5), (7, -4, 6), (8, 7), (9, 15, 8), (10, -2, 9), (10, 11), (11, 16, 12), (12, -1, 1)]], 'tensors': [['C1', 'T1_ket', 'T1_bra', 'C2', 'T2_ket', 'T2_bra', 'C3', 'T3_bra', 'T3_ket', 'C4', 'T4_bra', 'T4_ket'], 'ket_tensor']}

precondition_operator_triangular: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'mfZb,bgYc,chXi,ijWd,dkVe,elUm,fghjklT->ZYXWVUT', 'filter_additional_tensors': ['ket_tensor'], 'filter_peps_tensors': [['C1', 'C2', 'C3', 'C4', 'C5', 'C6']], 'ncon_network': [(12, 5, -1, 1), (1, 6, -2, 2), (2, 7, -3, 8), (8, 9, -4, 3), (3, 10, -5, 4), (4, 11, -6, 12), (5, 6, 7, 9, 10, 11, -7)], 'network': [[(12, 5, -1, 1), (1, 6, -2, 2), (2, 7, -3, 8), (8, 9, -4, 3), (3, 10, -5, 4), (4, 11, -6, 12)], (5, 6, 7, 9, 10, 11, -7)], 'network_additional_tensors': [(5, 6, 7, 9, 10, 11, -7)], 'network_peps_tensors': [[(12, 5, -1, 1), (1, 6, -2, 2), (2, 7, -3, 8), (8, 9, -4, 3), (3, 10, -5, 4), (4, 11, -6, 12)]], 'tensors': [['C1', 'C2', 'C3', 'C4', 'C5', 'C6'], 'ket_tensor']}

square_kagome_pess_mapping: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YXj,hWb,fVc,gUd,iTe,RSk,Zfb,Qic,kge,jhd->ZYXWVUTSRQ', 'filter_additional_tensors': ['t1', 't2', 't3', 't4', 't5', 't6', 'simplex_left', 'simplex_top', 'simplex_right', 'simplex_bottom'], 'filter_peps_tensors': [], 'ncon_network': [(-2, -3, 9), (7, -4, 1), (5, -5, 2), (6, -6, 3), (8, -7, 4), (-9, -8, 10), (-1, 5, 1), (-10, 8, 2), (10, 6, 4), (9, 7, 3)], 'network': [(-2, -3, 9), (7, -4, 1), (5, -5, 2), (6, -6, 3), (8, -7, 4), (-9, -8, 10), (-1, 5, 1), (-10, 8, 2), (10, 6, 4), (9, 7, 3)], 'network_additional_tensors': [(-2, -3, 9), (7, -4, 1), (5, -5, 2), (6, -6, 3), (8, -7, 4), (-9, -8, 10), (-1, 5, 1), (-10, 8, 2), (10, 6, 4), (9, 7, 3)], 'network_peps_tensors': [], 'tensors': ['t1', 't2', 't3', 't4', 't5', 't6', 'simplex_left', 'simplex_top', 'simplex_right', 'simplex_bottom']}

triangular_ctmrg_C1_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fmnYdej,iopXghj,behc,cfil,lmok,Zbdg,knpW->ZYXW', 'filter_additional_tensors': ['projector_150_left', 'projector_90_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'T1b']], 'ncon_network': [(5, 12, 13, -2, 3, 4, 9), (8, 14, 15, -3, 6, 7, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10), (-1, 1, 3, 6), (10, 13, 15, -4)], 'network': [[(5, 12, 13, -2, 3, 4, 9), (8, 14, 15, -3, 6, 7, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)], (-1, 1, 3, 6), (10, 13, 15, -4)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 13, 15, -4)], 'network_peps_tensors': [[(5, 12, 13, -2, 3, 4, 9), (8, 14, 15, -3, 6, 7, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'T1b'], 'projector_150_left', 'projector_90_right']}

triangular_ctmrg_C2_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efmnYdj,hiopXgj,behc,cfil,lmok,Zbdg,knpW->ZYXW', 'filter_additional_tensors': ['projector_90_left', 'projector_30_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'T2b']], 'ncon_network': [(4, 5, 12, 13, -2, 3, 9), (7, 8, 14, 15, -3, 6, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10), (-1, 1, 3, 6), (10, 13, 15, -4)], 'network': [[(4, 5, 12, 13, -2, 3, 9), (7, 8, 14, 15, -3, 6, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)], (-1, 1, 3, 6), (10, 13, 15, -4)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 13, 15, -4)], 'network_peps_tensors': [[(4, 5, 12, 13, -2, 3, 9), (7, 8, 14, 15, -3, 6, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'T2b'], 'projector_90_left', 'projector_30_right']}

triangular_ctmrg_C3_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defmnYj,ghiopXj,behc,cfil,lmok,Zbdg,knpW->ZYXW', 'filter_additional_tensors': ['projector_30_left', 'projector_330_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'T3b']], 'ncon_network': [(3, 4, 5, 12, 13, -2, 9), (6, 7, 8, 14, 15, -3, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10), (-1, 1, 3, 6), (10, 13, 15, -4)], 'network': [[(3, 4, 5, 12, 13, -2, 9), (6, 7, 8, 14, 15, -3, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)], (-1, 1, 3, 6), (10, 13, 15, -4)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 13, 15, -4)], 'network_peps_tensors': [[(3, 4, 5, 12, 13, -2, 9), (6, 7, 8, 14, 15, -3, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'T3b'], 'projector_30_left', 'projector_330_right']}

triangular_ctmrg_C4_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Ydefmnj,Xghiopj,behc,cfil,lmok,Zbdg,knpW->ZYXW', 'filter_additional_tensors': ['projector_330_left', 'projector_270_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'T4b']], 'ncon_network': [(-2, 3, 4, 5, 12, 13, 9), (-3, 6, 7, 8, 14, 15, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10), (-1, 1, 3, 6), (10, 13, 15, -4)], 'network': [[(-2, 3, 4, 5, 12, 13, 9), (-3, 6, 7, 8, 14, 15, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)], (-1, 1, 3, 6), (10, 13, 15, -4)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 13, 15, -4)], 'network_peps_tensors': [[(-2, 3, 4, 5, 12, 13, 9), (-3, 6, 7, 8, 14, 15, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'T4b'], 'projector_330_left', 'projector_270_right']}

triangular_ctmrg_C5_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'nYdefmj,pXghioj,behc,cfil,lmok,Zbdg,knpW->ZYXW', 'filter_additional_tensors': ['projector_270_left', 'projector_210_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'T5b']], 'ncon_network': [(13, -2, 3, 4, 5, 12, 9), (15, -3, 6, 7, 8, 14, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10), (-1, 1, 3, 6), (10, 13, 15, -4)], 'network': [[(13, -2, 3, 4, 5, 12, 9), (15, -3, 6, 7, 8, 14, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)], (-1, 1, 3, 6), (10, 13, 15, -4)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 13, 15, -4)], 'network_peps_tensors': [[(13, -2, 3, 4, 5, 12, 9), (15, -3, 6, 7, 8, 14, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'T5b'], 'projector_270_left', 'projector_210_right']}

triangular_ctmrg_C6_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'mnYdefj,opXghij,behc,cfil,lmok,Zbdg,knpW->ZYXW', 'filter_additional_tensors': ['projector_210_left', 'projector_150_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'T6b']], 'ncon_network': [(12, 13, -2, 3, 4, 5, 9), (14, 15, -3, 6, 7, 8, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10), (-1, 1, 3, 6), (10, 13, 15, -4)], 'network': [[(12, 13, -2, 3, 4, 5, 9), (14, 15, -3, 6, 7, 8, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)], (-1, 1, 3, 6), (10, 13, 15, -4)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 13, 15, -4)], 'network_peps_tensors': [[(12, 13, -2, 3, 4, 5, 9), (14, 15, -3, 6, 7, 8, 9), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 14, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'T6b'], 'projector_210_left', 'projector_150_right']}

triangular_ctmrg_T1_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eflWYdj,himVXgj,behc,cfik,Zbdg,klmU->ZYXWVU', 'filter_additional_tensors': ['projector_90_left', 'projector_90_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'T1b']], 'ncon_network': [(4, 5, 11, -4, -2, 3, 9), (7, 8, 12, -5, -3, 6, 9), (1, 4, 7, 2), (2, 5, 8, 10), (-1, 1, 3, 6), (10, 11, 12, -6)], 'network': [[(4, 5, 11, -4, -2, 3, 9), (7, 8, 12, -5, -3, 6, 9), (1, 4, 7, 2), (2, 5, 8, 10)], (-1, 1, 3, 6), (10, 11, 12, -6)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 11, 12, -6)], 'network_peps_tensors': [[(4, 5, 11, -4, -2, 3, 9), (7, 8, 12, -5, -3, 6, 9), (1, 4, 7, 2), (2, 5, 8, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'T1b'], 'projector_90_left', 'projector_90_right']}

triangular_ctmrg_T2_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'deflWYj,ghimVXj,behc,cfik,Zbdg,klmU->ZYXWVU', 'filter_additional_tensors': ['projector_30_left', 'projector_30_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'T2b']], 'ncon_network': [(3, 4, 5, 11, -4, -2, 9), (6, 7, 8, 12, -5, -3, 9), (1, 4, 7, 2), (2, 5, 8, 10), (-1, 1, 3, 6), (10, 11, 12, -6)], 'network': [[(3, 4, 5, 11, -4, -2, 9), (6, 7, 8, 12, -5, -3, 9), (1, 4, 7, 2), (2, 5, 8, 10)], (-1, 1, 3, 6), (10, 11, 12, -6)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 11, 12, -6)], 'network_peps_tensors': [[(3, 4, 5, 11, -4, -2, 9), (6, 7, 8, 12, -5, -3, 9), (1, 4, 7, 2), (2, 5, 8, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'T2b'], 'projector_30_left', 'projector_30_right']}

triangular_ctmrg_T3_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YdeflWj,XghimVj,behc,cfik,Zbdg,klmU->ZYXWVU', 'filter_additional_tensors': ['projector_330_left', 'projector_330_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'T3b']], 'ncon_network': [(-2, 3, 4, 5, 11, -4, 9), (-3, 6, 7, 8, 12, -5, 9), (1, 4, 7, 2), (2, 5, 8, 10), (-1, 1, 3, 6), (10, 11, 12, -6)], 'network': [[(-2, 3, 4, 5, 11, -4, 9), (-3, 6, 7, 8, 12, -5, 9), (1, 4, 7, 2), (2, 5, 8, 10)], (-1, 1, 3, 6), (10, 11, 12, -6)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 11, 12, -6)], 'network_peps_tensors': [[(-2, 3, 4, 5, 11, -4, 9), (-3, 6, 7, 8, 12, -5, 9), (1, 4, 7, 2), (2, 5, 8, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'T3b'], 'projector_330_left', 'projector_330_right']}

triangular_ctmrg_T4_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WYdeflj,VXghimj,behc,cfik,Zbdg,klmU->ZYXWVU', 'filter_additional_tensors': ['projector_270_left', 'projector_270_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'T4b']], 'ncon_network': [(-4, -2, 3, 4, 5, 11, 9), (-5, -3, 6, 7, 8, 12, 9), (1, 4, 7, 2), (2, 5, 8, 10), (-1, 1, 3, 6), (10, 11, 12, -6)], 'network': [[(-4, -2, 3, 4, 5, 11, 9), (-5, -3, 6, 7, 8, 12, 9), (1, 4, 7, 2), (2, 5, 8, 10)], (-1, 1, 3, 6), (10, 11, 12, -6)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 11, 12, -6)], 'network_peps_tensors': [[(-4, -2, 3, 4, 5, 11, 9), (-5, -3, 6, 7, 8, 12, 9), (1, 4, 7, 2), (2, 5, 8, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'T4b'], 'projector_270_left', 'projector_270_right']}

triangular_ctmrg_T5_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'lWYdefj,mVXghij,behc,cfik,Zbdg,klmU->ZYXWVU', 'filter_additional_tensors': ['projector_210_left', 'projector_210_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'T5b']], 'ncon_network': [(11, -4, -2, 3, 4, 5, 9), (12, -5, -3, 6, 7, 8, 9), (1, 4, 7, 2), (2, 5, 8, 10), (-1, 1, 3, 6), (10, 11, 12, -6)], 'network': [[(11, -4, -2, 3, 4, 5, 9), (12, -5, -3, 6, 7, 8, 9), (1, 4, 7, 2), (2, 5, 8, 10)], (-1, 1, 3, 6), (10, 11, 12, -6)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 11, 12, -6)], 'network_peps_tensors': [[(11, -4, -2, 3, 4, 5, 9), (12, -5, -3, 6, 7, 8, 9), (1, 4, 7, 2), (2, 5, 8, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'T5b'], 'projector_210_left', 'projector_210_right']}

triangular_ctmrg_T6_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'flWYdej,imVXghj,behc,cfik,Zbdg,klmU->ZYXWVU', 'filter_additional_tensors': ['projector_150_left', 'projector_150_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'T6b']], 'ncon_network': [(5, 11, -4, -2, 3, 4, 9), (8, 12, -5, -3, 6, 7, 9), (1, 4, 7, 2), (2, 5, 8, 10), (-1, 1, 3, 6), (10, 11, 12, -6)], 'network': [[(5, 11, -4, -2, 3, 4, 9), (8, 12, -5, -3, 6, 7, 9), (1, 4, 7, 2), (2, 5, 8, 10)], (-1, 1, 3, 6), (10, 11, 12, -6)], 'network_additional_tensors': [(-1, 1, 3, 6), (10, 11, 12, -6)], 'network_peps_tensors': [[(5, 11, -4, -2, 3, 4, 9), (8, 12, -5, -3, 6, 7, 9), (1, 4, 7, 2), (2, 5, 8, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'T6b'], 'projector_150_left', 'projector_150_right']}

triangular_ctmrg_T_proj_150_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'oYldefj,pXmghij,Zlmk,kdgb,behc,cfin,nopW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'C6', 'T6b']], 'ncon_network': [(14, -2, 11, 3, 4, 5, 9), (15, -3, 12, 6, 7, 8, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)], 'network': [[(14, -2, 11, 3, 4, 5, 9), (15, -3, 12, 6, 7, 8, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(14, -2, 11, 3, 4, 5, 9), (15, -3, 12, 6, 7, 8, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'C6', 'T6b']]}

triangular_ctmrg_T_proj_150_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'deflXoj,ghimWpj,Zopn,ndgb,behc,cfik,klmY->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'C3', 'T3b']], 'ncon_network': [(3, 4, 5, 11, -3, 14, 9), (6, 7, 8, 12, -4, 15, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)], 'network': [[(3, 4, 5, 11, -3, 14, 9), (6, 7, 8, 12, -4, 15, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, 11, -3, 14, 9), (6, 7, 8, 12, -4, 15, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'C3', 'T3b']]}

triangular_ctmrg_T_proj_210_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Yldefoj,Xmghipj,Zlmk,kdgb,behc,cfin,nopW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a_trunc', 'C3', 'C4', 'C5', 'T5b']], 'ncon_network': [(-2, 11, 3, 4, 5, 14, 9), (-3, 12, 6, 7, 8, 15, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)], 'network': [[(-2, 11, 3, 4, 5, 14, 9), (-3, 12, 6, 7, 8, 15, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 11, 3, 4, 5, 14, 9), (-3, 12, 6, 7, 8, 15, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T2a_trunc', 'C3', 'C4', 'C5', 'T5b']]}

triangular_ctmrg_T_proj_210_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'eflXodj,himWpgj,Zopn,ndgb,behc,cfik,klmY->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b_trunc']], 'ncon_network': [(4, 5, 11, -3, 14, 3, 9), (7, 8, 12, -4, 15, 6, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)], 'network': [[(4, 5, 11, -3, 14, 3, 9), (7, 8, 12, -4, 15, 6, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, 11, -3, 14, 3, 9), (7, 8, 12, -4, 15, 6, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b_trunc']]}

triangular_ctmrg_T_proj_270_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ldefoYj,mghipXj,Zlmk,kdgb,behc,cfin,nopW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'C4', 'T4b']], 'ncon_network': [(11, 3, 4, 5, 14, -2, 9), (12, 6, 7, 8, 15, -3, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)], 'network': [[(11, 3, 4, 5, 14, -2, 9), (12, 6, 7, 8, 15, -3, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(11, 3, 4, 5, 14, -2, 9), (12, 6, 7, 8, 15, -3, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'C4', 'T4b']]}

triangular_ctmrg_T_proj_270_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'flXodej,imWpghj,Zopn,ndgb,behc,cfik,klmY->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'C1', 'T1b']], 'ncon_network': [(5, 11, -3, 14, 3, 4, 9), (8, 12, -4, 15, 6, 7, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)], 'network': [[(5, 11, -3, 14, 3, 4, 9), (8, 12, -4, 15, 6, 7, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 11, -3, 14, 3, 4, 9), (8, 12, -4, 15, 6, 7, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'C1', 'T1b']]}

triangular_ctmrg_T_proj_30_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efoYldj,hipXmgj,Zlmk,kdgb,behc,cfin,nopW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b']], 'ncon_network': [(4, 5, 14, -2, 11, 3, 9), (7, 8, 15, -3, 12, 6, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)], 'network': [[(4, 5, 14, -2, 11, 3, 9), (7, 8, 15, -3, 12, 6, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, 14, -2, 11, 3, 9), (7, 8, 15, -3, 12, 6, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b']]}

triangular_ctmrg_T_proj_30_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Xodeflj,Wpghimj,Zopn,ndgb,behc,cfik,klmY->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'C5', 'T5b']], 'ncon_network': [(-3, 14, 3, 4, 5, 11, 9), (-4, 15, 6, 7, 8, 12, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)], 'network': [[(-3, 14, 3, 4, 5, 11, 9), (-4, 15, 6, 7, 8, 12, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-3, 14, 3, 4, 5, 11, 9), (-4, 15, 6, 7, 8, 12, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'C5', 'T5b']]}

triangular_ctmrg_T_proj_330_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defoYlj,ghipXmj,Zlmk,kdgb,behc,cfin,nopW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a_trunc', 'C1', 'C2', 'C3', 'T3b']], 'ncon_network': [(3, 4, 5, 14, -2, 11, 9), (6, 7, 8, 15, -3, 12, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)], 'network': [[(3, 4, 5, 14, -2, 11, 9), (6, 7, 8, 15, -3, 12, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, 14, -2, 11, 9), (6, 7, 8, 15, -3, 12, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T6a_trunc', 'C1', 'C2', 'C3', 'T3b']]}

triangular_ctmrg_T_proj_330_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'lXodefj,mWpghij,Zopn,ndgb,behc,cfik,klmY->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'C6', 'T6b_trunc']], 'ncon_network': [(11, -3, 14, 3, 4, 5, 9), (12, -4, 15, 6, 7, 8, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)], 'network': [[(11, -3, 14, 3, 4, 5, 9), (12, -4, 15, 6, 7, 8, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(11, -3, 14, 3, 4, 5, 9), (12, -4, 15, 6, 7, 8, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'C6', 'T6b_trunc']]}

triangular_ctmrg_T_proj_90_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'foYldej,ipXmghj,Zlmk,kdgb,behc,cfin,nopW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a_trunc', 'C5', 'C6', 'C1', 'T1b']], 'ncon_network': [(5, 14, -2, 11, 3, 4, 9), (8, 15, -3, 12, 6, 7, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)], 'network': [[(5, 14, -2, 11, 3, 4, 9), (8, 15, -3, 12, 6, 7, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 14, -2, 11, 3, 4, 9), (8, 15, -3, 12, 6, 7, 9), (-1, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T4a_trunc', 'C5', 'C6', 'C1', 'T1b']]}

triangular_ctmrg_T_proj_90_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'odeflXj,pghimWj,Zopn,ndgb,behc,cfik,klmY->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'C4', 'T4b_trunc']], 'ncon_network': [(14, 3, 4, 5, 11, -3, 9), (15, 6, 7, 8, 12, -4, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)], 'network': [[(14, 3, 4, 5, 11, -3, 9), (15, 6, 7, 8, 12, -4, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(14, 3, 4, 5, 11, -3, 9), (15, 6, 7, 8, 12, -4, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -2)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'C4', 'T4b_trunc']]}

triangular_ctmrg_corner_150: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dlVYefj,gmUXhij,Zehb,bfic,cdgk,klmW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'T1b']], 'ncon_network': [(3, 11, -5, -2, 4, 5, 9), (6, 12, -6, -3, 7, 8, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 10), (10, 11, 12, -4)], 'network': [[(3, 11, -5, -2, 4, 5, 9), (6, 12, -6, -3, 7, 8, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 10), (10, 11, 12, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 11, -5, -2, 4, 5, 9), (6, 12, -6, -3, 7, 8, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 10), (10, 11, 12, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'T1b']]}

triangular_ctmrg_corner_210: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'lVYefdj,mUXhigj,Zehb,bfic,cdgk,klmW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'T6b']], 'ncon_network': [(11, -5, -2, 4, 5, 3, 9), (12, -6, -3, 7, 8, 6, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 10), (10, 11, 12, -4)], 'network': [[(11, -5, -2, 4, 5, 3, 9), (12, -6, -3, 7, 8, 6, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 10), (10, 11, 12, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(11, -5, -2, 4, 5, 3, 9), (12, -6, -3, 7, 8, 6, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 10), (10, 11, 12, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'T6b']]}

triangular_ctmrg_corner_210_expectation: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'kTWefdZ,lSVhigY,Xehb,bfic,cdgj,jklU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'T6b']], 'ncon_network': [(10, -7, -4, 4, 5, 3, -1), (11, -8, -5, 7, 8, 6, -2), (-3, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 9), (9, 10, 11, -6)], 'network': [[(10, -7, -4, 4, 5, 3, -1), (11, -8, -5, 7, 8, 6, -2), (-3, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 9), (9, 10, 11, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(10, -7, -4, 4, 5, 3, -1), (11, -8, -5, 7, 8, 6, -2), (-3, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 9), (9, 10, 11, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'T6b']]}

triangular_ctmrg_corner_270: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'VYdeflj,UXghimj,Zdgb,behc,cfik,klmW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'T5b']], 'ncon_network': [(-5, -2, 3, 4, 5, 11, 9), (-6, -3, 6, 7, 8, 12, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)], 'network': [[(-5, -2, 3, 4, 5, 11, 9), (-6, -3, 6, 7, 8, 12, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-5, -2, 3, 4, 5, 11, 9), (-6, -3, 6, 7, 8, 12, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'T5b']]}

triangular_ctmrg_corner_30: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'deflVYj,ghimUXj,Zdgb,behc,cfik,klmW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'T3b']], 'ncon_network': [(3, 4, 5, 11, -5, -2, 9), (6, 7, 8, 12, -6, -3, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)], 'network': [[(3, 4, 5, 11, -5, -2, 9), (6, 7, 8, 12, -6, -3, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, 11, -5, -2, 9), (6, 7, 8, 12, -6, -3, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'T3b']]}

triangular_ctmrg_corner_330: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YdeflVj,XghimUj,Zdgb,behc,cfik,klmW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'T4b']], 'ncon_network': [(-2, 3, 4, 5, 11, -5, 9), (-3, 6, 7, 8, 12, -6, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)], 'network': [[(-2, 3, 4, 5, 11, -5, 9), (-3, 6, 7, 8, 12, -6, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 3, 4, 5, 11, -5, 9), (-3, 6, 7, 8, 12, -6, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'T4b']]}

triangular_ctmrg_corner_330_expectation: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WdefkTZ,VghilSY,Xdgb,behc,cfij,jklU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'T4b']], 'ncon_network': [(-4, 3, 4, 5, 10, -7, -1), (-5, 6, 7, 8, 11, -8, -2), (-3, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 9), (9, 10, 11, -6)], 'network': [[(-4, 3, 4, 5, 10, -7, -1), (-5, 6, 7, 8, 11, -8, -2), (-3, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 9), (9, 10, 11, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-4, 3, 4, 5, 10, -7, -1), (-5, 6, 7, 8, 11, -8, -2), (-3, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 9), (9, 10, 11, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'T4b']]}

triangular_ctmrg_corner_90: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'delVYfj,ghmUXij,Zfib,bdgc,cehk,klmW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'T2b']], 'ncon_network': [(3, 4, 11, -5, -2, 5, 9), (6, 7, 12, -6, -3, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 10), (10, 11, 12, -4)], 'network': [[(3, 4, 11, -5, -2, 5, 9), (6, 7, 12, -6, -3, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 10), (10, 11, 12, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 11, -5, -2, 5, 9), (6, 7, 12, -6, -3, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 10), (10, 11, 12, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'T2b']]}

triangular_ctmrg_corner_90_expectation: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dekTWfZ,ghlSViY,Xfib,bdgc,cehj,jklU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'T2b']], 'ncon_network': [(3, 4, 10, -7, -4, 5, -1), (6, 7, 11, -8, -5, 8, -2), (-3, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 9), (9, 10, 11, -6)], 'network': [[(3, 4, 10, -7, -4, 5, -1), (6, 7, 11, -8, -5, 8, -2), (-3, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 9), (9, 10, 11, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 10, -7, -4, 5, -1), (6, 7, 11, -8, -5, 8, -2), (-3, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 9), (9, 10, 11, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'T2b']]}

triangular_ctmrg_corrlen_absorb_120: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defYmnj,ghiXopj,cehb,bfiZ,Wmok,knpl,cdgl->ZYXW', 'filter_additional_tensors': ['vec'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'T2b', 'T5a', 'T5b']], 'ncon_network': [(3, 4, 5, -2, 12, 13, 9), (6, 7, 8, -3, 14, 15, 9), (2, 4, 7, 1), (1, 5, 8, -1), (-4, 12, 14, 10), (10, 13, 15, 11), [2, 3, 6, 11]], 'network': [[(3, 4, 5, -2, 12, 13, 9), (6, 7, 8, -3, 14, 15, 9), (2, 4, 7, 1), (1, 5, 8, -1), (-4, 12, 14, 10), (10, 13, 15, 11)], [2, 3, 6, 11]], 'network_additional_tensors': [[2, 3, 6, 11]], 'network_peps_tensors': [[(3, 4, 5, -2, 12, 13, 9), (6, 7, 8, -3, 14, 15, 9), (2, 4, 7, 1), (1, 5, 8, -1), (-4, 12, 14, 10), (10, 13, 15, 11)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'T2b', 'T5a', 'T5b'], 'vec']}

triangular_ctmrg_corrlen_absorb_180: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'deYmnfj,ghXopij,cdgb,behZ,Wmok,knpl,cfil->ZYXW', 'filter_additional_tensors': ['vec'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'T1b', 'T4a', 'T4b']], 'ncon_network': [(3, 4, -2, 12, 13, 5, 9), (6, 7, -3, 14, 15, 8, 9), (2, 3, 6, 1), (1, 4, 7, -1), (-4, 12, 14, 10), (10, 13, 15, 11), [2, 5, 8, 11]], 'network': [[(3, 4, -2, 12, 13, 5, 9), (6, 7, -3, 14, 15, 8, 9), (2, 3, 6, 1), (1, 4, 7, -1), (-4, 12, 14, 10), (10, 13, 15, 11)], [2, 5, 8, 11]], 'network_additional_tensors': [[2, 5, 8, 11]], 'network_peps_tensors': [[(3, 4, -2, 12, 13, 5, 9), (6, 7, -3, 14, 15, 8, 9), (2, 3, 6, 1), (1, 4, 7, -1), (-4, 12, 14, 10), (10, 13, 15, 11)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'T1b', 'T4a', 'T4b'], 'vec']}

triangular_ctmrg_corrlen_absorb_60: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'demnYfj,ghopXij,Zfib,bdgc,lmok,knpW,cehl->ZYXW', 'filter_additional_tensors': ['vec'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'T6b', 'T3a', 'T3b']], 'ncon_network': [(3, 4, 12, 13, -2, 5, 9), (6, 7, 14, 15, -3, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (11, 12, 14, 10), (10, 13, 15, -4), [2, 4, 7, 11]], 'network': [[(3, 4, 12, 13, -2, 5, 9), (6, 7, 14, 15, -3, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (11, 12, 14, 10), (10, 13, 15, -4)], [2, 4, 7, 11]], 'network_additional_tensors': [[2, 4, 7, 11]], 'network_peps_tensors': [[(3, 4, 12, 13, -2, 5, 9), (6, 7, 14, 15, -3, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (11, 12, 14, 10), (10, 13, 15, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'T6b', 'T3a', 'T3b'], 'vec']}

triangular_ctmrg_corrlen_vec_120: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efoYldj,hipXmgj,Wlmk,kdgb,behc,cfin,nopZ->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b']], 'ncon_network': [(4, 5, 14, -2, 11, 3, 9), (7, 8, 15, -3, 12, 6, 9), (-4, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -1)], 'network': [[(4, 5, 14, -2, 11, 3, 9), (7, 8, 15, -3, 12, 6, 9), (-4, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, 14, -2, 11, 3, 9), (7, 8, 15, -3, 12, 6, 9), (-4, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b']]}

triangular_ctmrg_corrlen_vec_180: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'foYldej,ipXmghj,Wlmk,kdgb,behc,cfin,nopZ->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'C1', 'T1b']], 'ncon_network': [(5, 14, -2, 11, 3, 4, 9), (8, 15, -3, 12, 6, 7, 9), (-4, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -1)], 'network': [[(5, 14, -2, 11, 3, 4, 9), (8, 15, -3, 12, 6, 7, 9), (-4, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 14, -2, 11, 3, 4, 9), (8, 15, -3, 12, 6, 7, 9), (-4, 11, 12, 10), (10, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 13), (13, 14, 15, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'C1', 'T1b']]}

triangular_ctmrg_corrlen_vec_60: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'deflYoj,ghimXpj,Zopn,ndgb,behc,cfik,klmW->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'C3', 'T3b']], 'ncon_network': [(3, 4, 5, 11, -2, 14, 9), (6, 7, 8, 12, -3, 15, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)], 'network': [[(3, 4, 5, 11, -2, 14, 9), (6, 7, 8, 12, -3, 15, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, 11, -2, 14, 9), (6, 7, 8, 12, -3, 15, 9), (-1, 14, 15, 13), (13, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 10), (10, 11, 12, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'C3', 'T3b']]}

triangular_ctmrg_next_nearest_2_pos_x_pos_y_expectation_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'VYdefhT,UXijklS,Zdib,bejc,cfkg,ghlW->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'T5b']], 'ncon_network': [(-5, -2, 3, 4, 5, 7, -7), (-6, -3, 8, 9, 10, 11, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)], 'network': [[(-5, -2, 3, 4, 5, 7, -7), (-6, -3, 8, 9, 10, 11, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-5, -2, 3, 4, 5, 7, -7), (-6, -3, 8, 9, 10, 11, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'T5b']]}

triangular_ctmrg_next_nearest_2_pos_x_pos_y_expectation_middle_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fYWTdej,iXVSghj,Udgb,behc,cfiZ->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'T6b']], 'ncon_network': [(5, -2, -4, -7, 3, 4, 9), (8, -3, -5, -8, 6, 7, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)], 'network': [[(5, -2, -4, -7, 3, 4, 9), (8, -3, -5, -8, 6, 7, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, -2, -4, -7, 3, 4, 9), (8, -3, -5, -8, 6, 7, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'T6b']]}

triangular_ctmrg_next_nearest_2_pos_x_pos_y_expectation_middle_left_open: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fYWTdeR,iXVSghQ,Udgb,behc,cfiZ->ZYXWVUTSRQ', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'T6b']], 'ncon_network': [(5, -2, -4, -7, 3, 4, -9), (8, -3, -5, -8, 6, 7, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)], 'network': [[(5, -2, -4, -7, 3, 4, -9), (8, -3, -5, -8, 6, 7, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, -2, -4, -7, 3, 4, -9), (8, -3, -5, -8, 6, 7, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'T6b']]}

triangular_ctmrg_next_nearest_2_pos_x_pos_y_expectation_middle_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YdefTWj,XghiSVj,Zdgb,behc,cfiU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'T3b']], 'ncon_network': [(-2, 3, 4, 5, -7, -4, 9), (-3, 6, 7, 8, -8, -5, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)], 'network': [[(-2, 3, 4, 5, -7, -4, 9), (-3, 6, 7, 8, -8, -5, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 3, 4, 5, -7, -4, 9), (-3, 6, 7, 8, -8, -5, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'T3b']]}

triangular_ctmrg_next_nearest_2_pos_x_pos_y_expectation_middle_right_open: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YdefTWR,XghiSVQ,Zdgb,behc,cfiU->ZYXWVUTSRQ', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'T3b']], 'ncon_network': [(-2, 3, 4, 5, -7, -4, -9), (-3, 6, 7, 8, -8, -5, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)], 'network': [[(-2, 3, 4, 5, -7, -4, -9), (-3, 6, 7, 8, -8, -5, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 3, 4, 5, -7, -4, -9), (-3, 6, 7, 8, -8, -5, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'T3b']]}

triangular_ctmrg_next_nearest_2_pos_x_pos_y_expectation_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efhTWdZ,jklSViY,Xdib,bejc,cfkg,ghlU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'T2b']], 'ncon_network': [(4, 5, 7, -7, -4, 3, -1), (9, 10, 11, -8, -5, 8, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)], 'network': [[(4, 5, 7, -7, -4, 3, -1), (9, 10, 11, -8, -5, 8, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, 7, -7, -4, 3, -1), (9, 10, 11, -8, -5, 8, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'T2b']]}

triangular_ctmrg_next_nearest_neg_x_pos_y_expectation_bottom_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'hTWdefZ,lSVijkY,Xdib,bejc,cfkg,ghlU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'T6b']], 'ncon_network': [(7, -7, -4, 3, 4, 5, -1), (11, -8, -5, 8, 9, 10, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)], 'network': [[(7, -7, -4, 3, 4, 5, -1), (11, -8, -5, 8, 9, 10, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(7, -7, -4, 3, 4, 5, -1), (11, -8, -5, 8, 9, 10, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'T6b']]}

triangular_ctmrg_next_nearest_neg_x_pos_y_expectation_bottom_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WTdefYj,VSghiXj,Udgb,behc,cfiZ->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'T4b']], 'ncon_network': [(-4, -7, 3, 4, 5, -2, 9), (-5, -8, 6, 7, 8, -3, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)], 'network': [[(-4, -7, 3, 4, 5, -2, 9), (-5, -8, 6, 7, 8, -3, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-4, -7, 3, 4, 5, -2, 9), (-5, -8, 6, 7, 8, -3, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'T4b']]}

triangular_ctmrg_next_nearest_neg_x_pos_y_expectation_bottom_right_open: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WTdefYR,VSghiXQ,Udgb,behc,cfiZ->ZYXWVUTSRQ', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'T4b']], 'ncon_network': [(-4, -7, 3, 4, 5, -2, -9), (-5, -8, 6, 7, 8, -3, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)], 'network': [[(-4, -7, 3, 4, 5, -2, -9), (-5, -8, 6, 7, 8, -3, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-4, -7, 3, 4, 5, -2, -9), (-5, -8, 6, 7, 8, -3, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'T4b']]}

triangular_ctmrg_next_nearest_neg_x_pos_y_expectation_top_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efTWYdj,hiSVXgj,Zdgb,behc,cfiU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'T1b']], 'ncon_network': [(4, 5, -7, -4, -2, 3, 9), (7, 8, -8, -5, -3, 6, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)], 'network': [[(4, 5, -7, -4, -2, 3, 9), (7, 8, -8, -5, -3, 6, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, -7, -4, -2, 3, 9), (7, 8, -8, -5, -3, 6, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'T1b']]}

triangular_ctmrg_next_nearest_neg_x_pos_y_expectation_top_left_open: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efTWYdR,hiSVXgQ,Zdgb,behc,cfiU->ZYXWVUTSRQ', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'T1b']], 'ncon_network': [(4, 5, -7, -4, -2, 3, -9), (7, 8, -8, -5, -3, 6, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)], 'network': [[(4, 5, -7, -4, -2, 3, -9), (7, 8, -8, -5, -3, 6, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, -7, -4, -2, 3, -9), (7, 8, -8, -5, -3, 6, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'T1b']]}

triangular_ctmrg_next_nearest_neg_x_pos_y_expectation_top_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defhVYT,ijklUXS,Zdib,bejc,cfkg,ghlW->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'T3b']], 'ncon_network': [(3, 4, 5, 7, -5, -2, -7), (8, 9, 10, 11, -6, -3, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)], 'network': [[(3, 4, 5, 7, -5, -2, -7), (8, 9, 10, 11, -6, -3, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, 7, -5, -2, -7), (8, 9, 10, 11, -6, -3, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'T3b']]}

triangular_ctmrg_next_nearest_pos_x_2_pos_y_expectation_bottom_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YWTdefj,XVSghij,Udgb,behc,cfiZ->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'T5b']], 'ncon_network': [(-2, -4, -7, 3, 4, 5, 9), (-3, -5, -8, 6, 7, 8, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)], 'network': [[(-2, -4, -7, 3, 4, 5, 9), (-3, -5, -8, 6, 7, 8, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, -4, -7, 3, 4, 5, 9), (-3, -5, -8, 6, 7, 8, 9), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'T5b']]}

triangular_ctmrg_next_nearest_pos_x_2_pos_y_expectation_bottom_left_open: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YWTdefR,XVSghiQ,Udgb,behc,cfiZ->ZYXWVUTSRQ', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'T5b']], 'ncon_network': [(-2, -4, -7, 3, 4, 5, -9), (-3, -5, -8, 6, 7, 8, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)], 'network': [[(-2, -4, -7, 3, 4, 5, -9), (-3, -5, -8, 6, 7, 8, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, -4, -7, 3, 4, 5, -9), (-3, -5, -8, 6, 7, 8, -10), (-6, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'T5b']]}

triangular_ctmrg_next_nearest_pos_x_2_pos_y_expectation_bottom_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YdefhVT,XijklUS,Zdib,bejc,cfkg,ghlW->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'T4b']], 'ncon_network': [(-2, 3, 4, 5, 7, -5, -7), (-3, 8, 9, 10, 11, -6, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)], 'network': [[(-2, 3, 4, 5, 7, -5, -7), (-3, 8, 9, 10, 11, -6, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 3, 4, 5, 7, -5, -7), (-3, 8, 9, 10, 11, -6, -8), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'T4b']]}

triangular_ctmrg_next_nearest_pos_x_2_pos_y_expectation_top_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fhTWdeZ,klSVijY,Xdib,bejc,cfkg,ghlU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'T1b']], 'ncon_network': [(5, 7, -7, -4, 3, 4, -1), (10, 11, -8, -5, 8, 9, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)], 'network': [[(5, 7, -7, -4, 3, 4, -1), (10, 11, -8, -5, 8, 9, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 7, -7, -4, 3, 4, -1), (10, 11, -8, -5, 8, 9, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'T1b']]}

triangular_ctmrg_next_nearest_pos_x_2_pos_y_expectation_top_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defTWYj,ghiSVXj,Zdgb,behc,cfiU->ZYXWVUTS', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'T2b']], 'ncon_network': [(3, 4, 5, -7, -4, -2, 9), (6, 7, 8, -8, -5, -3, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)], 'network': [[(3, 4, 5, -7, -4, -2, 9), (6, 7, 8, -8, -5, -3, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, -7, -4, -2, 9), (6, 7, 8, -8, -5, -3, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'T2b']]}

triangular_ctmrg_next_nearest_pos_x_2_pos_y_expectation_top_right_open: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defTWYR,ghiSVXQ,Zdgb,behc,cfiU->ZYXWVUTSRQ', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'T2b']], 'ncon_network': [(3, 4, 5, -7, -4, -2, -9), (6, 7, 8, -8, -5, -3, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)], 'network': [[(3, 4, 5, -7, -4, -2, -9), (6, 7, 8, -8, -5, -3, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, -7, -4, -2, -9), (6, 7, 8, -8, -5, -3, -10), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'T2b']]}

triangular_ctmrg_one_site_expectation: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fghjklZ,nopqrsY,mfnb,bgoc,chpi,ijqd,dkre,elsm->ZY', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'C2', 'C3', 'C4', 'C5', 'C6']], 'ncon_network': [(5, 6, 7, 9, 10, 11, -1), (13, 14, 15, 16, 17, 18, -2), (12, 5, 13, 1), (1, 6, 14, 2), (2, 7, 15, 8), (8, 9, 16, 3), (3, 10, 17, 4), (4, 11, 18, 12)], 'network': [[(5, 6, 7, 9, 10, 11, -1), (13, 14, 15, 16, 17, 18, -2), (12, 5, 13, 1), (1, 6, 14, 2), (2, 7, 15, 8), (8, 9, 16, 3), (3, 10, 17, 4), (4, 11, 18, 12)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 6, 7, 9, 10, 11, -1), (13, 14, 15, 16, 17, 18, -2), (12, 5, 13, 1), (1, 6, 14, 2), (2, 7, 15, 8), (8, 9, 16, 3), (3, 10, 17, 4), (4, 11, 18, 12)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'C2', 'C3', 'C4', 'C5', 'C6']]}

triangular_ctmrg_split_C1_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dijYefn,klrXpmn,bfmc,cdkh,hilg,Zop,obe,gjq,qrW->ZYXW', 'filter_additional_tensors': ['projector_150_bra_left', 'projector_150_ket_left', 'projector_90_ket_right', 'projector_90_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'T1b']], 'ncon_network': [(3, 8, 9, -2, 4, 5, 13), (10, 11, 17, -3, 15, 12, 13), (1, 5, 12, 2), (2, 3, 10, 7), (7, 8, 11, 6), (-1, 14, 15), (14, 1, 4), (6, 9, 16), (16, 17, -4)], 'network': [[(3, 8, 9, -2, 4, 5, 13), (10, 11, 17, -3, 15, 12, 13), (1, 5, 12, 2), (2, 3, 10, 7), (7, 8, 11, 6)], (-1, 14, 15), (14, 1, 4), (6, 9, 16), (16, 17, -4)], 'network_additional_tensors': [(-1, 14, 15), (14, 1, 4), (6, 9, 16), (16, 17, -4)], 'network_peps_tensors': [[(3, 8, 9, -2, 4, 5, 13), (10, 11, 17, -3, 15, 12, 13), (1, 5, 12, 2), (2, 3, 10, 7), (7, 8, 11, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'T1b'], 'projector_150_bra_left', 'projector_150_ket_left', 'projector_90_ket_right', 'projector_90_bra_right']}

triangular_ctmrg_split_C2_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'deijYfn,klmrXpn,bdkc,celh,himg,Zop,obf,gjq,qrW->ZYXW', 'filter_additional_tensors': ['projector_90_bra_left', 'projector_90_ket_left', 'projector_30_ket_right', 'projector_30_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'T2b']], 'ncon_network': [(3, 4, 8, 9, -2, 5, 13), (10, 11, 12, 17, -3, 15, 13), (1, 3, 10, 2), (2, 4, 11, 7), (7, 8, 12, 6), (-1, 14, 15), (14, 1, 5), (6, 9, 16), (16, 17, -4)], 'network': [[(3, 4, 8, 9, -2, 5, 13), (10, 11, 12, 17, -3, 15, 13), (1, 3, 10, 2), (2, 4, 11, 7), (7, 8, 12, 6)], (-1, 14, 15), (14, 1, 5), (6, 9, 16), (16, 17, -4)], 'network_additional_tensors': [(-1, 14, 15), (14, 1, 5), (6, 9, 16), (16, 17, -4)], 'network_peps_tensors': [[(3, 4, 8, 9, -2, 5, 13), (10, 11, 12, 17, -3, 15, 13), (1, 3, 10, 2), (2, 4, 11, 7), (7, 8, 12, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'T2b'], 'projector_90_bra_left', 'projector_90_ket_left', 'projector_30_ket_right', 'projector_30_bra_right']}

triangular_ctmrg_split_C3_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defhpYl,rijkoXl,beic,cfjg,ghkn,Zqr,qbd,nom,mpW->ZYXW', 'filter_additional_tensors': ['projector_30_bra_left', 'projector_30_ket_left', 'projector_330_bra_right', 'projector_330_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'T3b']], 'ncon_network': [(3, 4, 5, 7, 15, -2, 11), (17, 8, 9, 10, 14, -3, 11), (1, 4, 8, 2), (2, 5, 9, 6), (6, 7, 10, 13), (-1, 16, 17), (16, 1, 3), (13, 14, 12), (12, 15, -4)], 'network': [[(3, 4, 5, 7, 15, -2, 11), (17, 8, 9, 10, 14, -3, 11), (1, 4, 8, 2), (2, 5, 9, 6), (6, 7, 10, 13)], (-1, 16, 17), (16, 1, 3), (13, 14, 12), (12, 15, -4)], 'network_additional_tensors': [(-1, 16, 17), (16, 1, 3), (13, 14, 12), (12, 15, -4)], 'network_peps_tensors': [[(3, 4, 5, 7, 15, -2, 11), (17, 8, 9, 10, 14, -3, 11), (1, 4, 8, 2), (2, 5, 9, 6), (6, 7, 10, 13)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'T3b'], 'projector_30_bra_left', 'projector_30_ket_left', 'projector_330_bra_right', 'projector_330_ket_right']}

triangular_ctmrg_split_C4_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Ypklmrn,Xdefijn,bkec,clfh,hmig,Zop,obd,gjq,qrW->ZYXW', 'filter_additional_tensors': ['projector_330_ket_left', 'projector_330_bra_left', 'projector_270_bra_right', 'projector_270_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'T4b']], 'ncon_network': [(-2, 15, 10, 11, 12, 17, 13), (-3, 3, 4, 5, 8, 9, 13), (1, 10, 4, 2), (2, 11, 5, 7), (7, 12, 8, 6), (-1, 14, 15), (14, 1, 3), (6, 9, 16), (16, 17, -4)], 'network': [[(-2, 15, 10, 11, 12, 17, 13), (-3, 3, 4, 5, 8, 9, 13), (1, 10, 4, 2), (2, 11, 5, 7), (7, 12, 8, 6)], (-1, 14, 15), (14, 1, 3), (6, 9, 16), (16, 17, -4)], 'network_additional_tensors': [(-1, 14, 15), (14, 1, 3), (6, 9, 16), (16, 17, -4)], 'network_peps_tensors': [[(-2, 15, 10, 11, 12, 17, 13), (-3, 3, 4, 5, 8, 9, 13), (1, 10, 4, 2), (2, 11, 5, 7), (7, 12, 8, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'T4b'], 'projector_330_ket_left', 'projector_330_bra_left', 'projector_270_bra_right', 'projector_270_ket_right']}

triangular_ctmrg_split_C5_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'rYpklmn,jXdefin,bkec,clfh,hmig,Zop,obd,gjq,qrW->ZYXW', 'filter_additional_tensors': ['projector_270_ket_left', 'projector_270_bra_left', 'projector_210_bra_right', 'projector_210_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'T5b']], 'ncon_network': [(17, -2, 15, 10, 11, 12, 13), (9, -3, 3, 4, 5, 8, 13), (1, 10, 4, 2), (2, 11, 5, 7), (7, 12, 8, 6), (-1, 14, 15), (14, 1, 3), (6, 9, 16), (16, 17, -4)], 'network': [[(17, -2, 15, 10, 11, 12, 13), (9, -3, 3, 4, 5, 8, 13), (1, 10, 4, 2), (2, 11, 5, 7), (7, 12, 8, 6)], (-1, 14, 15), (14, 1, 3), (6, 9, 16), (16, 17, -4)], 'network_additional_tensors': [(-1, 14, 15), (14, 1, 3), (6, 9, 16), (16, 17, -4)], 'network_peps_tensors': [[(17, -2, 15, 10, 11, 12, 13), (9, -3, 3, 4, 5, 8, 13), (1, 10, 4, 2), (2, 11, 5, 7), (7, 12, 8, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'T5b'], 'projector_270_ket_left', 'projector_270_bra_left', 'projector_210_bra_right', 'projector_210_ket_right']}

triangular_ctmrg_split_C6_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ioYrjkl,hpXdefl,bjec,ckfg,gihn,Zqr,qbd,nom,mpW->ZYXW', 'filter_additional_tensors': ['projector_210_ket_left', 'projector_210_bra_left', 'projector_150_ket_right', 'projector_150_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'T6b']], 'ncon_network': [(8, 14, -2, 17, 9, 10, 11), (7, 15, -3, 3, 4, 5, 11), (1, 9, 4, 2), (2, 10, 5, 6), (6, 8, 7, 13), (-1, 16, 17), (16, 1, 3), (13, 14, 12), (12, 15, -4)], 'network': [[(8, 14, -2, 17, 9, 10, 11), (7, 15, -3, 3, 4, 5, 11), (1, 9, 4, 2), (2, 10, 5, 6), (6, 8, 7, 13)], (-1, 16, 17), (16, 1, 3), (13, 14, 12), (12, 15, -4)], 'network_additional_tensors': [(-1, 16, 17), (16, 1, 3), (13, 14, 12), (12, 15, -4)], 'network_peps_tensors': [[(8, 14, -2, 17, 9, 10, 11), (7, 15, -3, 3, 4, 5, 11), (1, 9, 4, 2), (2, 10, 5, 6), (6, 8, 7, 13)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'T6b'], 'projector_210_ket_left', 'projector_210_bra_left', 'projector_150_ket_right', 'projector_150_bra_right']}

triangular_ctmrg_split_T1_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dehWYfm,jkoVXlm,bdjc,cekg,Zil,ibf,ghn,noU->ZYXWVU', 'filter_additional_tensors': ['projector_90_bra_left', 'projector_90_ket_left', 'projector_90_ket_right', 'projector_90_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'T1b']], 'ncon_network': [(3, 4, 7, -4, -2, 5, 12), (9, 10, 14, -5, -3, 11, 12), (1, 3, 9, 2), (2, 4, 10, 6), (-1, 8, 11), (8, 1, 5), (6, 7, 13), (13, 14, -6)], 'network': [[(3, 4, 7, -4, -2, 5, 12), (9, 10, 14, -5, -3, 11, 12), (1, 3, 9, 2), (2, 4, 10, 6)], (-1, 8, 11), (8, 1, 5), (6, 7, 13), (13, 14, -6)], 'network_additional_tensors': [(-1, 8, 11), (8, 1, 5), (6, 7, 13), (13, 14, -6)], 'network_peps_tensors': [[(3, 4, 7, -4, -2, 5, 12), (9, 10, 14, -5, -3, 11, 12), (1, 3, 9, 2), (2, 4, 10, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'T1b'], 'projector_90_bra_left', 'projector_90_ket_left', 'projector_90_ket_right', 'projector_90_bra_right']}

triangular_ctmrg_split_T2_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defhWYm,jkloVXm,bekc,cflg,Zij,ibd,ghn,noU->ZYXWVU', 'filter_additional_tensors': ['projector_30_bra_left', 'projector_30_ket_left', 'projector_30_ket_right', 'projector_30_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'T2b']], 'ncon_network': [(3, 4, 5, 7, -4, -2, 12), (9, 10, 11, 14, -5, -3, 12), (1, 4, 10, 2), (2, 5, 11, 6), (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network': [[(3, 4, 5, 7, -4, -2, 12), (9, 10, 11, 14, -5, -3, 12), (1, 4, 10, 2), (2, 5, 11, 6)], (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_additional_tensors': [(-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_peps_tensors': [[(3, 4, 5, 7, -4, -2, 12), (9, 10, 11, 14, -5, -3, 12), (1, 4, 10, 2), (2, 5, 11, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'T2b'], 'projector_30_bra_left', 'projector_30_ket_left', 'projector_30_ket_right', 'projector_30_bra_right']}

triangular_ctmrg_split_T3_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YjkloWm,XdefhVm,bkec,clfg,Zij,ibd,ghn,noU->ZYXWVU', 'filter_additional_tensors': ['projector_330_ket_left', 'projector_330_bra_left', 'projector_330_bra_right', 'projector_330_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'T3b']], 'ncon_network': [(-2, 9, 10, 11, 14, -4, 12), (-3, 3, 4, 5, 7, -5, 12), (1, 10, 4, 2), (2, 11, 5, 6), (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network': [[(-2, 9, 10, 11, 14, -4, 12), (-3, 3, 4, 5, 7, -5, 12), (1, 10, 4, 2), (2, 11, 5, 6)], (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_additional_tensors': [(-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_peps_tensors': [[(-2, 9, 10, 11, 14, -4, 12), (-3, 3, 4, 5, 7, -5, 12), (1, 10, 4, 2), (2, 11, 5, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'T3b'], 'projector_330_ket_left', 'projector_330_bra_left', 'projector_330_bra_right', 'projector_330_ket_right']}

triangular_ctmrg_split_T4_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WYjklom,VXdefhm,bkec,clfg,Zij,ibd,ghn,noU->ZYXWVU', 'filter_additional_tensors': ['projector_270_ket_left', 'projector_270_bra_left', 'projector_270_bra_right', 'projector_270_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'T4b']], 'ncon_network': [(-4, -2, 9, 10, 11, 14, 12), (-5, -3, 3, 4, 5, 7, 12), (1, 10, 4, 2), (2, 11, 5, 6), (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network': [[(-4, -2, 9, 10, 11, 14, 12), (-5, -3, 3, 4, 5, 7, 12), (1, 10, 4, 2), (2, 11, 5, 6)], (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_additional_tensors': [(-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_peps_tensors': [[(-4, -2, 9, 10, 11, 14, 12), (-5, -3, 3, 4, 5, 7, 12), (1, 10, 4, 2), (2, 11, 5, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'T4b'], 'projector_270_ket_left', 'projector_270_bra_left', 'projector_270_bra_right', 'projector_270_ket_right']}

triangular_ctmrg_split_T5_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'oWYjklm,hVXdefm,bkec,clfg,Zij,ibd,ghn,noU->ZYXWVU', 'filter_additional_tensors': ['projector_210_ket_left', 'projector_210_bra_left', 'projector_210_bra_right', 'projector_210_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'T5b']], 'ncon_network': [(14, -4, -2, 9, 10, 11, 12), (7, -5, -3, 3, 4, 5, 12), (1, 10, 4, 2), (2, 11, 5, 6), (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network': [[(14, -4, -2, 9, 10, 11, 12), (7, -5, -3, 3, 4, 5, 12), (1, 10, 4, 2), (2, 11, 5, 6)], (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_additional_tensors': [(-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_peps_tensors': [[(14, -4, -2, 9, 10, 11, 12), (7, -5, -3, 3, 4, 5, 12), (1, 10, 4, 2), (2, 11, 5, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'T5b'], 'projector_210_ket_left', 'projector_210_bra_left', 'projector_210_bra_right', 'projector_210_ket_right']}

triangular_ctmrg_split_T6_absorption: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fhWYdem,loVXjkm,bekc,cflg,Zij,ibd,ghn,noU->ZYXWVU', 'filter_additional_tensors': ['projector_150_bra_left', 'projector_150_ket_left', 'projector_150_ket_right', 'projector_150_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'T6b']], 'ncon_network': [(5, 7, -4, -2, 3, 4, 12), (11, 14, -5, -3, 9, 10, 12), (1, 4, 10, 2), (2, 5, 11, 6), (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network': [[(5, 7, -4, -2, 3, 4, 12), (11, 14, -5, -3, 9, 10, 12), (1, 4, 10, 2), (2, 5, 11, 6)], (-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_additional_tensors': [(-1, 8, 9), (8, 1, 3), (6, 7, 13), (13, 14, -6)], 'network_peps_tensors': [[(5, 7, -4, -2, 3, 4, 12), (11, 14, -5, -3, 9, 10, 12), (1, 4, 10, 2), (2, 5, 11, 6)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'T6b'], 'projector_150_bra_left', 'projector_150_ket_left', 'projector_150_ket_right', 'projector_150_bra_right']}

triangular_ctmrg_split_corner_150: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'knqYijl,hoWdefl,biec,cjfg,gkhm,mnop,Zbd,pqX->ZYXW', 'filter_additional_tensors': ['proj_210_bra_left', 'proj_90_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'T1b']], 'ncon_network': [(10, 13, 16, -2, 8, 9, 11), (7, 14, -4, 3, 4, 5, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15), (-1, 1, 3), (15, 16, -3)], 'network': [[(10, 13, 16, -2, 8, 9, 11), (7, 14, -4, 3, 4, 5, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15)], (-1, 1, 3), (15, 16, -3)], 'network_additional_tensors': [(-1, 1, 3), (15, 16, -3)], 'network_peps_tensors': [[(10, 13, 16, -2, 8, 9, 11), (7, 14, -4, 3, 4, 5, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'T1b'], 'proj_210_bra_left', 'proj_90_ket_right']}

triangular_ctmrg_split_corner_210: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'nqYijkl,oWdefhl,biec,cjfg,gkhm,mnop,Zbd,pqX->ZYXW', 'filter_additional_tensors': ['proj_270_bra_left', 'proj_150_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'T6b']], 'ncon_network': [(13, 16, -2, 8, 9, 10, 11), (14, -4, 3, 4, 5, 7, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15), (-1, 1, 3), (15, 16, -3)], 'network': [[(13, 16, -2, 8, 9, 10, 11), (14, -4, 3, 4, 5, 7, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15)], (-1, 1, 3), (15, 16, -3)], 'network_additional_tensors': [(-1, 1, 3), (15, 16, -3)], 'network_peps_tensors': [[(13, 16, -2, 8, 9, 10, 11), (14, -4, 3, 4, 5, 7, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'T6b'], 'proj_270_bra_left', 'proj_150_ket_right']}

triangular_ctmrg_split_corner_270: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'WYijknl,qdefhol,biec,cjfg,gkhm,mnop,Zbd,pqX->ZYXW', 'filter_additional_tensors': ['proj_330_bra_left', 'proj_210_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'T5b']], 'ncon_network': [(-4, -2, 8, 9, 10, 13, 11), (16, 3, 4, 5, 7, 14, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15), (-1, 1, 3), (15, 16, -3)], 'network': [[(-4, -2, 8, 9, 10, 13, 11), (16, 3, 4, 5, 7, 14, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15)], (-1, 1, 3), (15, 16, -3)], 'network_additional_tensors': [(-1, 1, 3), (15, 16, -3)], 'network_peps_tensors': [[(-4, -2, 8, 9, 10, 13, 11), (16, 3, 4, 5, 7, 14, 11), (1, 8, 4, 2), (2, 9, 5, 6), (6, 10, 7, 12), (12, 13, 14, 15)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'T5b'], 'proj_330_bra_left', 'proj_210_bra_right']}

triangular_ctmrg_split_corner_30: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dehnWfl,ijkoqYl,bdic,cejg,ghkm,mnop,Zbf,pqX->ZYXW', 'filter_additional_tensors': ['proj_90_ket_left', 'proj_330_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'T3b']], 'ncon_network': [(3, 4, 7, 13, -4, 5, 11), (8, 9, 10, 14, 16, -2, 11), (1, 3, 8, 2), (2, 4, 9, 6), (6, 7, 10, 12), (12, 13, 14, 15), (-1, 1, 5), (15, 16, -3)], 'network': [[(3, 4, 7, 13, -4, 5, 11), (8, 9, 10, 14, 16, -2, 11), (1, 3, 8, 2), (2, 4, 9, 6), (6, 7, 10, 12), (12, 13, 14, 15)], (-1, 1, 5), (15, 16, -3)], 'network_additional_tensors': [(-1, 1, 5), (15, 16, -3)], 'network_peps_tensors': [[(3, 4, 7, 13, -4, 5, 11), (8, 9, 10, 14, 16, -2, 11), (1, 3, 8, 2), (2, 4, 9, 6), (6, 7, 10, 12), (12, 13, 14, 15)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'T3b'], 'proj_90_ket_left', 'proj_330_bra_right']}

triangular_ctmrg_split_corner_330: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fdehnWl,Yijkoql,bdic,cejg,ghkm,mnop,Zbf,pqX->ZYXW', 'filter_additional_tensors': ['proj_30_ket_left', 'proj_270_bra_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'T4b']], 'ncon_network': [(5, 3, 4, 7, 13, -4, 11), (-2, 8, 9, 10, 14, 16, 11), (1, 3, 8, 2), (2, 4, 9, 6), (6, 7, 10, 12), (12, 13, 14, 15), (-1, 1, 5), (15, 16, -3)], 'network': [[(5, 3, 4, 7, 13, -4, 11), (-2, 8, 9, 10, 14, 16, 11), (1, 3, 8, 2), (2, 4, 9, 6), (6, 7, 10, 12), (12, 13, 14, 15)], (-1, 1, 5), (15, 16, -3)], 'network_additional_tensors': [(-1, 1, 5), (15, 16, -3)], 'network_peps_tensors': [[(5, 3, 4, 7, 13, -4, 11), (-2, 8, 9, 10, 14, 16, 11), (1, 3, 8, 2), (2, 4, 9, 6), (6, 7, 10, 12), (12, 13, 14, 15)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'T4b'], 'proj_30_ket_left', 'proj_270_bra_right']}

triangular_ctmrg_split_corner_90: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dhnqefl,ijoWYkl,bfkc,cdig,ghjm,mnop,Zbe,pqX->ZYXW', 'filter_additional_tensors': ['proj_150_ket_left', 'proj_30_ket_right'], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'T2b']], 'ncon_network': [(3, 7, 13, 16, 4, 5, 11), (8, 9, 14, -4, -2, 10, 11), (1, 5, 10, 2), (2, 3, 8, 6), (6, 7, 9, 12), (12, 13, 14, 15), (-1, 1, 4), (15, 16, -3)], 'network': [[(3, 7, 13, 16, 4, 5, 11), (8, 9, 14, -4, -2, 10, 11), (1, 5, 10, 2), (2, 3, 8, 6), (6, 7, 9, 12), (12, 13, 14, 15)], (-1, 1, 4), (15, 16, -3)], 'network_additional_tensors': [(-1, 1, 4), (15, 16, -3)], 'network_peps_tensors': [[(3, 7, 13, 16, 4, 5, 11), (8, 9, 14, -4, -2, 10, 11), (1, 5, 10, 2), (2, 3, 8, 6), (6, 7, 9, 12), (12, 13, 14, 15)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'T2b'], 'proj_150_ket_left', 'proj_30_ket_right']}

triangular_ctmrg_split_proj_150_330_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'oWdefmj,pYghinj,Zdgb,behc,cfil,lmnk,kopX->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'C6', 'T6b']], 'ncon_network': [(14, -4, 3, 4, 5, 12, 9), (15, -2, 6, 7, 8, 13, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)], 'network': [[(14, -4, 3, 4, 5, 12, 9), (15, -2, 6, 7, 8, 13, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(14, -4, 3, 4, 5, 12, 9), (15, -2, 6, 7, 8, 13, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'C6', 'T6b']]}

triangular_ctmrg_split_proj_150_330_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'demoYfj,ghnpWij,Zfib,bdgc,cehl,lmnk,kopX->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'C3', 'T3b']], 'ncon_network': [(3, 4, 12, 14, -2, 5, 9), (6, 7, 13, 15, -4, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 11), (11, 12, 13, 10), (10, 14, 15, -3)], 'network': [[(3, 4, 12, 14, -2, 5, 9), (6, 7, 13, 15, -4, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 12, 14, -2, 5, 9), (6, 7, 13, 15, -4, 8, 9), (-1, 5, 8, 1), (1, 3, 6, 2), (2, 4, 7, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'C3', 'T3b']]}

triangular_ctmrg_split_proj_30_210_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'dmoWefj,gnpYhij,Zehb,bfic,cdgl,lmnk,kopX->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b']], 'ncon_network': [(3, 12, 14, -4, 4, 5, 9), (6, 13, 15, -2, 7, 8, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 11), (11, 12, 13, 10), (10, 14, 15, -3)], 'network': [[(3, 12, 14, -4, 4, 5, 9), (6, 13, 15, -2, 7, 8, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 12, 14, -4, 4, 5, 9), (6, 13, 15, -2, 7, 8, 9), (-1, 4, 7, 1), (1, 5, 8, 2), (2, 3, 6, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b']]}

triangular_ctmrg_split_proj_30_210_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Ydefmoj,Wghinpj,Zdgb,behc,cfil,lmnk,kopX->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'C5', 'T5b']], 'ncon_network': [(-2, 3, 4, 5, 12, 14, 9), (-4, 6, 7, 8, 13, 15, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)], 'network': [[(-2, 3, 4, 5, 12, 14, 9), (-4, 6, 7, 8, 13, 15, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 3, 4, 5, 12, 14, 9), (-4, 6, 7, 8, 13, 15, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'C5', 'T5b']]}

triangular_ctmrg_split_proj_90_270_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'moWdefj,npYghij,Zdgb,behc,cfil,lmnk,kopX->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'C1', 'T1b']], 'ncon_network': [(12, 14, -4, 3, 4, 5, 9), (13, 15, -2, 6, 7, 8, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)], 'network': [[(12, 14, -4, 3, 4, 5, 9), (13, 15, -2, 6, 7, 8, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(12, 14, -4, 3, 4, 5, 9), (13, 15, -2, 6, 7, 8, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'C1', 'T1b']]}

triangular_ctmrg_split_proj_90_270_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defmoYj,ghinpWj,Zdgb,behc,cfil,lmnk,kopX->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'C4', 'T4b']], 'ncon_network': [(3, 4, 5, 12, 14, -2, 9), (6, 7, 8, 13, 15, -4, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)], 'network': [[(3, 4, 5, 12, 14, -2, 9), (6, 7, 8, 13, 15, -4, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, 12, 14, -2, 9), (6, 7, 8, 13, 15, -4, 9), (-1, 3, 6, 1), (1, 4, 7, 2), (2, 5, 8, 11), (11, 12, 13, 10), (10, 14, 15, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'C4', 'T4b']]}

triangular_ctmrg_two_site_expectation_diagonal_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'YdefhnV,XijkloU,Wdib,bejc,cfkg,ghlm,mnoZ->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'C5', 'T5b']], 'ncon_network': [(-2, 3, 4, 5, 7, 13, -5), (-3, 8, 9, 10, 11, 14, -6), (-4, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -1)], 'network': [[(-2, 3, 4, 5, 7, 13, -5), (-3, 8, 9, 10, 11, 14, -6), (-4, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-2, 3, 4, 5, 7, 13, -5), (-3, 8, 9, 10, 11, 14, -6), (-4, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T2a', 'C3', 'C4', 'C5', 'T5b']]}

triangular_ctmrg_two_site_expectation_diagonal_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fhnWdeZ,kloVijY,Xdib,bejc,cfkg,ghlm,mnoU->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b']], 'ncon_network': [(5, 7, 13, -4, 3, 4, -1), (10, 11, 14, -5, 8, 9, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -6)], 'network': [[(5, 7, 13, -4, 3, 4, -1), (10, 11, 14, -5, 8, 9, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 7, 13, -4, 3, 4, -1), (10, 11, 14, -5, 8, 9, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T5a', 'C6', 'C1', 'C2', 'T2b']]}

triangular_ctmrg_two_site_expectation_horizontal_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'hnWdefZ,loVijkY,Udib,bejc,cfkg,ghlm,mnoX->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'C1', 'T1b']], 'ncon_network': [(7, 13, -4, 3, 4, 5, -1), (11, 14, -5, 8, 9, 10, -2), (-6, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -3)], 'network': [[(7, 13, -4, 3, 4, 5, -1), (11, 14, -5, 8, 9, 10, -2), (-6, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -3)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(7, 13, -4, 3, 4, 5, -1), (11, 14, -5, 8, 9, 10, -2), (-6, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -3)]], 'tensors': [['tensor', 'tensor_conj', 'T4a', 'C5', 'C6', 'C1', 'T1b']]}

triangular_ctmrg_two_site_expectation_horizontal_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'defhnYV,ijkloXU,Zdib,bejc,cfkg,ghlm,mnoW->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'C4', 'T4b']], 'ncon_network': [(3, 4, 5, 7, 13, -2, -5), (8, 9, 10, 11, 14, -3, -6), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -4)], 'network': [[(3, 4, 5, 7, 13, -2, -5), (8, 9, 10, 11, 14, -3, -6), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -4)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(3, 4, 5, 7, 13, -2, -5), (8, 9, 10, 11, 14, -3, -6), (-1, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -4)]], 'tensors': [['tensor', 'tensor_conj', 'T1a', 'C2', 'C3', 'C4', 'T4b']]}

triangular_ctmrg_two_site_expectation_vertical_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'nYdefhV,oXijklU,Wdib,bejc,cfkg,ghlm,mnoZ->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'C6', 'T6b']], 'ncon_network': [(13, -2, 3, 4, 5, 7, -5), (14, -3, 8, 9, 10, 11, -6), (-4, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -1)], 'network': [[(13, -2, 3, 4, 5, 7, -5), (14, -3, 8, 9, 10, 11, -6), (-4, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(13, -2, 3, 4, 5, 7, -5), (14, -3, 8, 9, 10, 11, -6), (-4, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -1)]], 'tensors': [['tensor', 'tensor_conj', 'T3a', 'C4', 'C5', 'C6', 'T6b']]}

triangular_ctmrg_two_site_expectation_vertical_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efhnWdZ,jkloViY,Xdib,bejc,cfkg,ghlm,mnoU->ZYXWVU', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'C3', 'T3b']], 'ncon_network': [(4, 5, 7, 13, -4, 3, -1), (9, 10, 11, 14, -5, 8, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -6)], 'network': [[(4, 5, 7, 13, -4, 3, -1), (9, 10, 11, 14, -5, 8, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -6)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, 7, 13, -4, 3, -1), (9, 10, 11, 14, -5, 8, -2), (-3, 3, 8, 1), (1, 4, 9, 2), (2, 5, 10, 6), (6, 7, 11, 12), (12, 13, 14, -6)]], 'tensors': [['tensor', 'tensor_conj', 'T6a', 'C1', 'C2', 'C3', 'T3b']]}

triangular_pess_mapping: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'ZbYX,VbW->ZYXWV', 'filter_additional_tensors': ['site', 'simplex'], 'filter_peps_tensors': [], 'ncon_network': [(-1, 1, -2, -3), (-5, 1, -4)], 'network': [(-1, 1, -2, -3), (-5, 1, -4)], 'network_additional_tensors': [(-1, 1, -2, -3), (-5, 1, -4)], 'network_peps_tensors': [], 'tensors': ['site', 'simplex']}

unitcell_bond_dim_change_bottom: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'efliZ,ghljW,ijcX,kc,bkhf,bd,dgeY->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T2', 'C3', 'T3', 'C4', 'T4']], 'ncon_network': [(4, 5, 11, 8, -1), (6, 7, 11, 9, -4), (8, 9, 2, -3), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -2)], 'network': [[(4, 5, 11, 8, -1), (6, 7, 11, 9, -4), (8, 9, 2, -3), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(4, 5, 11, 8, -1), (6, 7, 11, 9, -4), (8, 9, 2, -3), (10, 2), (1, 10, 7, 5), (1, 3), (3, 6, 4, -2)]], 'tensors': [['tensor', 'tensor_conj', 'T2', 'C3', 'T3', 'C4', 'T4']]}

unitcell_bond_dim_change_left: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'fjlWe,hklXg,bd,degZ,cYkj,ci,ihfb->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'T3', 'C4', 'T4']], 'ncon_network': [(5, 9, 11, -4, 4), (7, 10, 11, -3, 6), (1, 3), (3, 4, 6, -1), (2, -2, 10, 9), (2, 8), (8, 7, 5, 1)], 'network': [[(5, 9, 11, -4, 4), (7, 10, 11, -3, 6), (1, 3), (3, 4, 6, -1), (2, -2, 10, 9), (2, 8), (8, 7, 5, 1)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(5, 9, 11, -4, 4), (7, 10, 11, -3, 6), (1, 3), (3, 4, 6, -1), (2, -2, 10, 9), (2, 8), (8, 7, 5, 1)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'T3', 'C4', 'T4']]}

unitcell_bond_dim_change_right: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'Zilfe,Wjlhg,Yegd,db,fhkb,Xcji,ck->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2', 'T3', 'C3']], 'ncon_network': [(-1, 8, 11, 5, 4), (-4, 9, 11, 7, 6), (-2, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-3, 2, 9, 8), (2, 10)], 'network': [[(-1, 8, 11, 5, 4), (-4, 9, 11, 7, 6), (-2, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-3, 2, 9, 8), (2, 10)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(-1, 8, 11, 5, 4), (-4, 9, 11, 7, 6), (-2, 4, 6, 3), (3, 1), (5, 7, 10, 1), (-3, 2, 9, 8), (2, 10)]], 'tensors': [['tensor', 'tensor_conj', 'T1', 'C2', 'T2', 'T3', 'C3']]}

unitcell_bond_dim_change_top: Dict[str, List[List[str | List[str]] | List[Tuple[int] | List[Tuple[int]]]]] = {'einsum_network': 'iWlef,jXlgh,ck,kfhb,bd,egYd,Zjic->ZYXW', 'filter_additional_tensors': [], 'filter_peps_tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'T4']], 'ncon_network': [(8, -4, 11, 4, 5), (9, -3, 11, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -2, 3), (-1, 9, 8, 2)], 'network': [[(8, -4, 11, 4, 5), (9, -3, 11, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -2, 3), (-1, 9, 8, 2)]], 'network_additional_tensors': [], 'network_peps_tensors': [[(8, -4, 11, 4, 5), (9, -3, 11, 6, 7), (2, 10), (10, 5, 7, 1), (1, 3), (4, 6, -2, 3), (-1, 9, 8, 2)]], 'tensors': [['tensor', 'tensor_conj', 'C1', 'T1', 'C2', 'T2', 'T4']]}