Symmetry-resolved entanglement in symmetry-protected topological phases

TL;DR

This paper develops a cohomology-based framework to analyze symmetry-resolved entanglement in symmetry-protected topological phases, revealing universal entanglement properties across dimensions.

Contribution

It introduces a general method to compute symmetry-resolved entanglement in SPTs using path integrals and group cocycles, unifying topological classification with entanglement analysis.

Findings

Universal degeneracies in entanglement spectrum of 1D SPTs

Decomposition of reduced density matrix into symmetry sectors

Applicable to all 1D topological phases with finite Abelian symmetries

Abstract

Symmetry protected topological phases (SPTs) have universal degeneracies in the entanglement spectrum in one dimension (1D). Here, we formulate this phenomenon in the framework of symmetry-resolved entanglement (SRE) using cohomology theory. We develop a general approach to compute entanglement measures of SPTs in any dimension and specifically SRE via a discrete path integral on multi-sheet Riemann surfaces with generalized defects. The resulting path integral is expressed in terms of group cocycles describing the topological actions of SPTs. Their cohomology classification allows to identify universal entanglement properties. Specifically, we demonstrate an equi-block decomposition of the reduced density matrix into symmetry sectors, for all 1D topological phases protected by finite Abelian unitary symmetries.