Long range order and symmetry breaking in Projected Entangled Pair State models

TL;DR

This paper investigates how PEPS models with $ ext{Z}_2$ symmetry exhibit long-range order and spontaneous symmetry breaking, linking these phenomena to transfer operator spectra and tensor properties, and deriving local entanglement Hamiltonians.

Contribution

It provides a characterization of symmetry broken states in PEPS and shows how to restore locality of the entanglement Hamiltonian across gapped phases.

Findings

Long-range order correlates with degeneracy in the transfer operator spectrum.

Spontaneous symmetry breaking arises from transfer operator perturbations.

Symmetry broken states enable derivation of local entanglement Hamiltonians.

Abstract

Projected Entangled Pair States (PEPS) provide a framework for the construction of models where a single tensor gives rise to both Hamiltonian and ground state wavefunction on the same footing. A key problem is to characterize the behavior which emerges in the system in terms of the properties of the tensor, and thus of the Hamiltonian. In this paper, we consider PEPS models with $\mathbb Z_2$ on-site symmetry and study the occurence of long-range order and spontaneous symmetry breaking. We show how long-range order is connected to a degeneracy in the spectrum of the PEPS transfer operator, and how the latter gives rise to spontaneous symmetry breaking under perturbations. We provide a succinct characterization of the symmetry broken states in terms of the PEPS tensor, and find that using the symmetry broken states we can derive a local entanglement Hamiltonian, thereby restoring locality of the entanglement Hamiltonian for all gapped phases.