Variational methods for contracting projected entangled-pair states
Abstract
The norms or expectation values of infinite projected entangled-pair states (PEPS) cannot be computed exactly, and approximation algorithms have to be applied. In the last years, many efficient algorithms have been devised -- the corner transfer matrix renormalization group (CTMRG) and variational uniform matrix product state (VUMPS) algorithm are the most common -- but it remains unclear whether they always lead to the same results. In this paper, we identify a subclass of PEPS for which we can reformulate the contraction as a variational problem that is algorithm independent. We use this variational feature to assess and compare the accuracy of CTMRG and VUMPS contractions. Moreover, we devise a new variational contraction scheme, which we can extend to compute general N-point correlation functions.
Cite
@article{arxiv.2110.12726,
title = {Variational methods for contracting projected entangled-pair states},
author = {Laurens Vanderstraeten and Lander Burgelman and Boris Ponsioen and Maarten Van Damme and Bram Vanhecke and Philippe Corboz and Jutho Haegeman and Frank Verstraete},
journal= {arXiv preprint arXiv:2110.12726},
year = {2022}
}