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arXiv · 1907.05490

A Classical Model Correspondence for G-symmetric Random Tensor Networks

Erica Morgan·Fernando G. S. L. Brandão
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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.

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Erica Morgan, Fernando G. S. L. Brandão. 2021-02-22. A Classical Model Correspondence for G-symmetric Random Tensor Networks. https://arxiv.org/abs/1907.05490

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