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A Classical Model Correspondence for G-symmetric Random Tensor Networks

Morgan, Eric and Brandão, Fernando G. S. L. (2019) A Classical Model Correspondence for G-symmetric Random Tensor Networks. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190801-134548265

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Abstract

We consider the scaling of entanglement entropy in random Projected Entangled Pairs States (PEPS) with an internal symmetry given by a finite group G. We systematically demonstrate a correspondence between this entanglement entropy and the difference of free energies of a classical Ising model with an addition non-local term. This non-local term counts the number of domain walls in a particular configuration of the classical spin model. We argue that for that overwhelming majority of such states, this gives rise to an area law scaling with well-defined topological entanglement entropy. The topological entanglement entropy is shown to be log|G| for a simply connected region A and which manifests as a difference in the number of domain walls of ground state energies for the two spin models.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1907.05490arXivDiscussion Paper
ORCID:
AuthorORCID
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:This work is part of IQIM, which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant PHY-1733907).
Group:Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFPHY-1733907
Record Number:CaltechAUTHORS:20190801-134548265
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190801-134548265
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97603
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Aug 2019 21:34
Last Modified:04 Jun 2020 10:14

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