Symmetry-resolved entanglement of 2D symmetry-protected topological states

TL;DR

This paper develops tensor network methods to analyze symmetry-resolved entanglement in 2D symmetry-protected topological states, revealing universal features and spectral flow behaviors in their entanglement spectra.

Contribution

It introduces tensor network techniques to study large 2D SPT states and tracks entanglement evolution under phase deformations using cohomology formalism.

Findings

Entanglement spectra are described by the same conformal field theory.

Spectral flow occurs with the insertion of a many-body Aharonov-Bohm flux.

Method successfully applied to the Levin-Gu model.

Abstract

Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely unexplored. However, addressing this problem numerically requires system sizes beyond the reach of exact diagonalization. Here, we develop tensor network methods that can access much larger systems and determine universal and nonuniversal features in their entanglement. Specifically, we construct one-dimensional matrix product operators that encapsulate all the entanglement data of two-dimensional symmetry-protected topological states. We first demonstrate our approach for the Levin-Gu model. Next, we use the cohomology formalism to deform the phase away from the fine-tuned point and track the evolution of its entanglement features and their symmetry resolution. The entanglement spectra are always described by the same conformal field theory. However, the levels undergo a spectral flow in accordance with an insertion of a many-body Aharonov-Bohm flux.