• Open Access

How local is the information in tensor networks of matrix product states or projected entangled pairs states

Anurag Anshu, Itai Arad, and Aditya Jain
Phys. Rev. B 94, 195143 – Published 28 November 2016

Abstract

Two-dimensional tensor networks such as projected entangled pairs states (PEPS) are generally hard to contract. This is arguably the main reason why variational tensor network methods in two dimensions are still not as successful as in one dimension. However, this is not necessarily the case if the tensor network represents a gapped ground state of a local Hamiltonian; such states are subject to many constraints and contain much more structure. In this paper, we introduce an approach for approximating the expectation value of a local observable in ground states of local Hamiltonians that are represented by PEPS tensor networks. Instead of contracting the full tensor network, we try to estimate the expectation value using only a local patch of the tensor network around the observable. Surprisingly, we demonstrate that this is often easier to do when the system is frustrated. In such case, the spanning vectors of the local patch are subject to nontrivial constraints that can be utilized via a semidefinite program to calculate rigorous lower and upper bounds on the expectation value. We test our approach in one-dimensional systems, where we show how the expectation value can be calculated up to at least 3 or 4 digits of precision, even when the patch radius is smaller than the correlation length.

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  • Received 1 April 2016

DOI:https://doi.org/10.1103/PhysRevB.94.195143

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Anurag Anshu and Itai Arad*

  • Centre for Quantum Technologies, National University of Singapore, Singapore

Aditya Jain

  • Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology-Hyderabad, India

  • *arad.itai@fastmail.com

Article Text

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Issue

Vol. 94, Iss. 19 — 15 November 2016

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