variPEPS -- Versatile tensor network library for variational ground state simulations in two spatial dimensions.

variPEPS is the Python variant of the 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 publications listed at the end of this readme.

Installation

Installation using pip

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

$ python3 -m pip install variPEPS

Usage

For detailed information how to use the package we want to point out to the documentation of the project.

Citation

We are happy if you want to use the framework for your research. For the citation of our work we ask to use the following references (the publications with the method description and the Zenodo reference for this Git repository):

• J. Naumann, E. L. Weerda, M. Rizzi, J. Eisert, and P. Schmoll, An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation, SciPost Phys. Lect. Notes 86 (2024), doi:10.21468/SciPostPhysLectNotes.86.
• J. Naumann, E. L. Weerda, J. Eisert, M. Rizzi and P. Schmoll, Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach, Phys. Rev. B 111, 235116 (2025), doi:10.1103/PhysRevB.111.235116.
• J. Naumann, J. Eisert, P. Schmoll, Variational optimization of projected entangled-pair states on the triangular lattice, arXiv:2510.04907
• J. Naumann, P. Schmoll, R. Losada, F. Wilde, and F. Krein, variPEPS (Python version), Zenodo.

The BibTeX code for these references are:

@article{10.21468/SciPostPhysLectNotes.86,
	title={{An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation}},
	author={Jan Naumann and Erik Lennart Weerda and Matteo Rizzi and Jens Eisert and Philipp Schmoll},
	journal={SciPost Phys. Lect. Notes},
	pages={86},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysLectNotes.86},
	url={https://scipost.org/10.21468/SciPostPhysLectNotes.86},
}

@article{PhysRevB.111.235116,
    title = {Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach},
    author = {Naumann, Jan and Weerda, Erik L. and Eisert, Jens and Rizzi, Matteo and Schmoll, Philipp},
    journal = {Phys. Rev. B},
    volume = {111},
    issue = {23},
    pages = {235116},
    numpages = {12},
    year = {2025},
    month = {Jun},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevB.111.235116},
    url = {https://link.aps.org/doi/10.1103/PhysRevB.111.235116}
}

@misc{naumann2025variationaloptimizationprojectedentangledpair,
    title={Variational optimization of projected entangled-pair states on the triangular lattice},
    author={Jan Naumann and Jens Eisert and Philipp Schmoll},
    year={2025},
    eprint={2510.04907},
    archivePrefix={arXiv},
    primaryClass={cond-mat.str-el},
    url={https://arxiv.org/abs/2510.04907},
}

@software{naumann_varipeps_python,
    author =        {Jan Naumann and Philipp Schmoll and Roberto Losada and Frederik Wilde and Finn Krein},
    title =         {{variPEPS (Python version)}},
    howpublished =  {Zenodo},
    url =           {https://doi.org/10.5281/ZENODO.10852390},
    doi =           {10.5281/ZENODO.10852390},
}