Non-abelian symmetry-resolved entanglement entropy

TL;DR

This paper develops a mathematical framework for symmetry-resolved entanglement entropy in systems with non-abelian symmetries, revealing new phenomena like entropy asymmetry due to non-abelian charge interactions.

Contribution

It introduces a novel approach to define and compute symmetry-resolved entanglement entropy for non-abelian groups, extending previous abelian-focused methods.

Findings

Derived exact formulas for average and variance of entanglement entropy

Identified asymmetry of entanglement entropy under subsystem exchange

Computed the Page curve for a system with SU(2) symmetry

Abstract

We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the abelian case, new phenomena arise from the interplay of locality and non-abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with SU(2) symmetry.