Edge--Entanglement correspondence for gapped topological phases with symmetry

TL;DR

This paper explores the relationship between edge theories and entanglement spectra in gapped, topologically ordered phases with symmetry, revealing how entanglement encodes edge properties and their stability under perturbations.

Contribution

It introduces an exactly solvable lattice model for a $\

Findings

Entanglement Hamiltonian encodes edge state information.

The correspondence between entanglement spectrum and edge theory is quantitatively characterized.

Edge theories and entanglement Hamiltonians are connected through RG flow analysis.

Abstract

The correspondence between the edge theory and the entanglement spectrum is firmly established for the chiral topological phases. We study gapped, topologically ordered, non-chiral states with a conserved $U(1)$ charge and show that the entanglement Hamiltonian contains not only the information about topologically distinct edges such phases may admit, but also which of them will be realized in the presence of symmetry breaking/conserving perturbations. We introduce an exactly solvable, charge conserving lattice model of a $\mathbb{Z}_2$ spin liquid and derive its edge theory and the entanglement Hamiltonian, also in the presence of perturbations. We construct a field theory of the edge and study its RG flow. We show the precise extent of the correspondence between the information contained in the entanglement Hamiltonian and the edge theory.