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

Abstract

We consider the problem of the decomposition of the Rényi 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 Rényi entropies exhibits a universal form related to the underlying symmetry group of the model, i.e. the dimension of the Lie group.

arXiv comment31 pages, v2: minor changes

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