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.

Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models / Calabrese, P.; Dubail, P.; Murciano, S.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2021:10(2021), pp. 1-32. [10.1007/JHEP10(2021)067]

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

Calabrese, P.;Murciano, S.
2021-01-01

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.
2021
2021
10
1
32
067
10.1007/JHEP10(2021)067
http://arxiv.org/abs/2106.15946v2
Calabrese, P.; Dubail, P.; Murciano, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128395
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