Implementation of line search methods for the CTMRG variational optimization (varipeps.optimization.line_search)

exception varipeps.optimization.line_search.NoSuitableStepSizeError

Bases: Exception

varipeps.optimization.line_search.line_search(input_tensors: Sequence[Array], unitcell: PEPS_Unit_Cell, expectation_func: Expectation_Model, gradient: Array, descent_direction: Array, current_value: float | Array, last_step_size: float | Array | None = None, convert_to_unitcell_func: Map_To_PEPS_Model | None = None, generate_unitcell: bool = False, spiral_indices: Sequence[int] | None = None, additional_input: Dict[str, Array] = {}, reinitialize_env_as_identities: bool = True) → Tuple[List[Array], PEPS_Unit_Cell, float | Array, float | Array]

Run two-way backtracing line search method for the CTMRG routine.

Parameters:

• input_tensors (sequence of jax.numpy.ndarray) – Sequence of the current tensors which should be optimized.

• unitcell (PEPS_Unit_Cell) – The PEPS unitcell to work on.

• expectation_func (Expectation_Model) – Callable to calculate one expectation value which is used as loss loss function of the model. Likely the function to calculate the energy.

• gradient (jax.numpy.ndarray) – The gradient of the CTMRG method and expectation function for the current step.

• descent_direction (jax.numpy.ndarray) – The descent direction which should be used for the line search.

• current_value (float or jax.numpy.ndarray) – The current value of the evaluation of the expectation function.

• last_step_size (float or jax.numpy.ndarray, optional) – The step size found in the last line search.

  Default: None

• convert_to_unitcell_func (Map_To_PEPS_Model, optional) – Function to convert the input_tensors to a PEPS unitcell. If ommited, it is assumed that a PEPS unitcell is the input.

  Default: None

• generate_unitcell (bool, optional) – Force generation of unitcell from new tensors

  Default: False

• spiral_indices (sequence of int, optional) – If spiral iPEPS ansatz is used, this argument contains the indices of the wave vectors in the input tensor list.

  Default: None

• additional_input (dict of str to jax.numpy.ndarray mapping, optional) – Dict with additional inputs which should be considered in the calculation of the expectation value.

  Default: {}

• reinitialize_env_as_identities (bool, optional) – Flag if the env tensors should be reinitialized with identities.

  Default: True

Returns:

Tuple with the optimized tensors, the new unitcell, the reduced expectation value and the step size found in the line search.

Return type:

tuple(list(jax.numpy.ndarray), PEPS_Unit_Cell, float, float)

Raises:

• ValueError – The parameters mismatch the expected inputs.

• RuntimeError – The line search does not converge.