Introduction

variPEPS is a Python tensor network library developed for variational ground state simulations in two spatial dimensions applying gradient optimization using automatic differentation.

For a detailed report on the method, please see our open-access publication on SciPost (doi:10.21468/SciPostPhysLectNotes.86).

Installation using pip

The current version of the variPEPS Python package is available on PyPI. It can be easily installed using the Python package manager pip:

$ python3 -m pip install variPEPS

Core Features

  • Calculation of expectation values, structure factors, overlaps and correlation lengths of infinite PEPS states.

  • Variational optimization for ground state search of Hamiltonian models using automatic differentiation.

  • Predefined mappings of other lattices (kagome, maple-leaf, …) to square and triangular PEPS structure.

  • Support for spiral-PEPS method (Phys. Rev. Lett. 133, 176502 (2024)).

  • Reference implementation of the split-CTMRG (Phys. Rev. B 111, 235116 (2025)) and triangular-CTMRG (Phys. Rev. B 113, 045117 (2026)) variants.

  • Direct support of just-in-time compilation (JIT) and GPU devices thanks to the jax framework.

Usage

The varipeps module is organized in several submodules corresponding to the different features. For a variational optimization the most important parts are (a full overview can be found in the variPEPS API reference):

  • varipeps.peps: To define iPEPS unit cell and the tensors on each site, the library provides in this submodule the abstractions to define such a unit cell.

  • varipeps.expectation: In this submodule the helper functions to define and calculate common expecation functions on the iPEPS unit cell. Particularly, the function can be used to define the Hamiltonian terms of the model of interest.

  • varipeps.mapping: If not only interactions on the square lattice are of interest but also models on other 2d lattices, in this submodule one can find mappings of other lattices. Also the files there can be a good starting point to implement even more lattices.

  • varipeps.optimization: The submodule providing the optimization algorithm and interface of the library. In almost all cases, one will interact with this part by the main function varipeps.optimization.optimize_peps_network or the convience wrapper around t.

All these different modules can be seen in action in the Overview section of the documentation where exemplary code is discussed in detail.

Citation

We are happy if you want to use the framework for your research. To cite our work we provide a list of our preferred references on the GitHub page of the project. Please check there for a current list.