Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

TL;DR

This paper analyzes how entanglement entropy decomposes in non-abelian symmetric theories, specifically Wess-Zumino-Witten models, revealing universal symmetry-related contributions and equipartition at leading order.

Contribution

It provides a detailed analysis of symmetry-resolved entanglement in WZW models, generalizing from SU(2) to arbitrary non-abelian groups, and identifies universal logarithmic contributions.

Findings

Entanglement is equally distributed among irreducible representation sectors at leading order.

A non-universal term depends only on the representation dimension.

Universal a ext{log} ext{log} L contribution related to the symmetry group.

Abstract

We consider the problem of the decomposition of the R\'enyi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider $SU(2)_k$ as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size $L$ the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on $L$ but only on the dimension of the representation. Moreover, a $\log\log L$ contribution to the R\'enyi entropies exhibits a universal form related to the underlying symmetry group of the model, i.e. the dimension of the Lie group.