Theory of noninteracting fermions and bosons in the canonical ensemble

Barghathi, Hatem; Yu, Jiangyong; Maestro, Adrian Del

doi:10.1103/physrevresearch.2.043206

Cited by 29 publications

(21 citation statements)

References 81 publications

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“…The possibility of measuring in an experiment the internal symmetry structure of the entanglement [20][21][22] went together with new theoretical frameworks developed to address the same problem [23,24]. These progresses paved the way to study different symmetryresolved contributions in various theoretical contexts such as CFTs [23][24][25][26][27][28][29], free [30,32] and interacting integrable quantum field theories [31,33], holographic settings [34], spin chains [21,22,[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], disordered systems [53][54][55][56] and for non-trivial topological phases [57][58][59].…”

Section: Introductionmentioning

confidence: 99%

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

Calabrese,

Dubail,

Murciano

2021

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

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

Calabrese,

Dubail,

Murciano

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The possibility of measuring in an experiment the internal symmetry structure of the entanglement [20][21][22][23] went together with new theoretical frameworks developed to address the same problem [24,25]. These progresses paved the way to study different symmetryresolved contributions in various theoretical contexts such as CFTs [24][25][26][27][28][29][30][31], free [32,34] and interacting integrable quantum field theories [33,35], holographic settings [36,37], spin chains [21,22,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54], disordered systems [55][56][57][58] and for non-trivial topological phases [59][60][61].…”

Section: Jhep10(2021)067mentioning

confidence: 99%

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

Calabrese

Dubail

Murciano

2021

J. High Energ. Phys.

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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 prefactor equal to half the dimension of the Lie group.

show abstract

“…The possibility of measuring in an experiment the internal symmetry structure of the entanglement [27,[31][32][33] was supported by new theoretical frameworks developed to address this problem [29,30]. These progresses allowed to deal with the resolution of entanglement in various theoretical contexts such as CFTs [29,30,[34][35][36][37][38][39][40][41][42][43], free [44,45] and interacting integrable quantum field theories [46][47][48], holographic settings [49][50][51][52], spin chains [27,28,32,[53][54][55][56][57][58][59][60][61][62][63][64], out-ofequilibrium contexts [65][66][67], disordered systems [68][69]…”

Section: Introductionmentioning

confidence: 99%

Symmetry-resolved entanglement in a long-range free-fermion chain

Ares,

Murciano,

Calabrese

2022

Preprint

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We investigate the symmetry resolution of entanglement in the presence of longrange couplings. To this end, we study the symmetry-resolved entanglement entropy in the ground state of a fermionic chain that has dimerised long-range hoppings with power-like decaying amplitude -a long-range generalisation of the Su-Schrieffer-Heeger model. This is a system that preserves the number of particles. The entropy of each symmetry sector is calculated via the charged moments of the reduced density matrix. We exploit some recent results on block Toeplitz determinants generated by a discontinuous symbol to obtain analytically the asymptotic behaviour of the charged moments and of the symmetry-resolved entropies for a large subsystem. At leading order we find entanglement equipartition, but comparing with the short-range counterpart its breaking occurs at a different order and it does depend on the hopping amplitudes.

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Theory of noninteracting fermions and bosons in the canonical ensemble

Cited by 29 publications

References 81 publications

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

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

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

Symmetry-resolved entanglement in a long-range free-fermion chain

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