A Classical Model Correspondence for G-symmetric Random Tensor Networks
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.
Cite
@article{arxiv.1907.05490,
title = {A Classical Model Correspondence for G-symmetric Random Tensor Networks},
author = {Erica Morgan and Fernando G. S. L. Brandão},
journal= {arXiv preprint arXiv:1907.05490},
year = {2021}
}