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

• URL: http://arxiv.org/abs/2106.15946v2
• Date: Fri, 15 Oct 2021 12:13:36 GMT
• Title: Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
• Authors: Pasquale Calabrese, J\'er\^ome Dubail and Sara Murciano
• Abstract summary: We first consider $SU(2)_k$ as a case study and then generalise to an arbitrary non-abelian Lie group. A $loglog L$ contribution to the R'enyi entropies exhibits a universal form related to the underlying symmetry group of the model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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