Variational methods for contracting projected entangled-pair states

• URL: http://arxiv.org/abs/2110.12726v2
• Date: Tue, 7 Jun 2022 09:17:21 GMT
• Title: Variational methods for contracting projected entangled-pair states
• Authors: Laurens Vanderstraeten, Lander Burgelman, Boris Ponsioen, Maarten Van Damme, Bram Vanhecke, Philippe Corboz, Jutho Haegeman and Frank Verstraete
• Abstract summary: 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. We devise a new variational contraction scheme, which we can extend to compute general N-point correlation functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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