Symmetry-resolved entanglement in symmetry-protected topological phases

Azses, Daniel; Sela, Eran

doi:10.1103/physrevb.102.235157

Cited by 70 publications

(40 citation statements)

References 76 publications

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“…over a large range of values of the local charge, the symmetry-resolved entropies are independent of the charge. The study of symmetry-resolved entanglement entropies has been applied to a variety of situations [6][7][8][9][10][11][12][13][14][15][16][17]. For quantum computing, these entropies also serve as building blocks for the definition of operationally accessible entanglement [18,19].…”

Section: Introductionmentioning

confidence: 99%

Finite-size corrections in critical symmetry-resolved entanglement

2021

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In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.

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Section: Introductionmentioning

confidence: 99%

Finite-size corrections in critical symmetry-resolved entanglement

2021

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“…Second, let us also mention a similarity between our entanglement entropy definition and recent work on symmetry resolved entanglement [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70]. Symmetry resolved entanglement is defined for a system with a global symmetry, for instance particle number conservation.…”

Section: Jhep10(2021)187mentioning

confidence: 91%

Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure

Gerbershagen

2021

J. High Energ. Phys.

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We define a generalized entanglement measure in the context of the AdS/CFT correspondence. Compared to the ordinary entanglement entropy for a spatial subregion dual to the area of the Ryu-Takayanagi surface, we take into account both entanglement between spatial degrees of freedom as well as between different fields of the boundary theory. Moreover, we resolve the contribution to the entanglement entropy of strings with different winding numbers in the bulk geometry. We then calculate this generalized entanglement measure in a thermal state dual to the BTZ black hole in the setting of the D1/D5 system at and close to the orbifold point. We find that the entanglement entropy defined in this way is dual to the length of a geodesic with non-zero winding number. Such geodesics probe the entire bulk geometry, including the entanglement shadow up to the horizon in the one-sided black hole as well as the wormhole growth in the case of a two-sided black hole for an arbitrarily long time. Therefore, we propose that the entanglement structure of the boundary state is enough to reconstruct asymptotically AdS3 geometries up to extremal surface barriers.

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“…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.

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Symmetry-resolved entanglement in symmetry-protected topological phases

Cited by 70 publications

References 76 publications

Finite-size corrections in critical symmetry-resolved entanglement

Finite-size corrections in critical symmetry-resolved entanglement

Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure

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

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