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arXiv · 2110.12726

Variational methods for contracting projected entangled-pair states

Laurens Vanderstraeten·Lander Burgelman·Boris Ponsioen·Maarten Van Damme·Bram Vanhecke·Philippe Corboz·Jutho Haegeman·Frank Verstraete
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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.

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Laurens Vanderstraeten, Lander Burgelman, Boris Ponsioen, Maarten Van Damme, Bram Vanhecke, Philippe Corboz, Jutho Haegeman, Frank Verstraete. 2021-10-25. Variational methods for contracting projected entangled-pair states. https://doi.org/10.1103/physrevb.105.195140

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