Dynamics of charge-resolved entanglement after a local quench

We present a thorough analysis of the entanglement entropies related to different symmetry sectors of free quantum field theories (QFT) with an internal U(1) symmetry. We provide explicit analytic computations for the charged moments of Dirac and complex scalar fields in two spacetime dimensions, both in the massive and massless cases, using two different approaches. The first one is based on the replica trick, the computation of the partition function on Riemann surfaces with the insertion of a flux α, and the introduction of properly modified twist fields, whose two-point function directly gives the scaling limit of the charged moments. With the second method, the diagonalisation in replica space maps the problem to the computation of a partition function on a cut plane, that can be written exactly in terms of the solutions of non-linear differential equations of the Painlevé V type. Within this approach, we also derive an asymptotic expansion for the short and long distance behaviour of the charged moments. Finally, the Fourier transform provides the desired symmetry resolved entropies: at the leading order, they satisfy entanglement equipartition and we identify the subleading terms that break it. Our analytical findings are tested against exact numerical calculations in lattice models.

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“…where we defined 15) and ρ z n (α) is defined so that ρ z n (α) = O(α 4 ). Notice, as we already stressed a few times, that in eq.…”

Section: The Expansion Close To the Conformal Point M =mentioning

confidence: 99%

Entanglement and symmetry resolution in two dimensional free quantum field theories

Murciano

Giulio

Calabrese

2020

J. High Energ. Phys.

119

127

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“…Only in very recent times, it became clear that it is also important to understand the relation between entanglement and symmetries and in particular how entanglement is shared between the various symmetry sectors of a theory [26][27][28]. To date there are many results concerning critical systems [28][29][30][31][32][33][34][35], but none for gapped ones (with the exception of Ref. [34] for a discrete symmetry, but here we are interested in continuous ones).…”

Section: Introductionmentioning

confidence: 99%

Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

2020

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We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U (1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results. arXiv:1911.09588v2 [cond-mat.stat-mech]

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“…Although there has already been a large interest in the entanglement of quantum systems with internal symmetries for clean systems [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], disordered models lack completely an analytical understanding of the symmetry resolved entanglement spectroscopy (with the notable exception of the nonequilibrium experiment in Ref. [34]).…”

Section: Introductionmentioning

confidence: 99%

Entanglement equipartition in critical random spin chains

et al. 2020

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The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement entropy for one-dimensional conformal and integrable systems. In this paper, we extend this equipartition theorem to the disordered critical systems by studying the random singlet phase. We analytically compute the disorder averaged symmetry resolved Rényi entropies and show the leading orders are independent of the symmetry sector. Our findings are cross-checked with simulations within the numerical strong disorder renormalization group. We also identify the first subleading term breaking equipartition which is of the form s 2 / ln where s is the magnetization of a subsystem of length .

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Dynamics of charge-resolved entanglement after a local quench

Cited by 103 publications

References 89 publications

Entanglement and symmetry resolution in two dimensional free quantum field theories

Entanglement and symmetry resolution in two dimensional free quantum field theories

Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

Entanglement equipartition in critical random spin chains

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