A classical model correspondence for G-symmetric random tensor networks. (21st October 2021) - Morgan, Erica; G S L Brandão, Fernando
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 then make use of this correspondence to argue for an area law scaling with well-defined topological entanglement entropy when the bond dimensions are sufficiently large. The topological entanglement entropy is shown to be log ∣ G ∣ for a simply connected region and results from a difference in the number of domain walls of ground state energies for the two spin models.