Entanglement and diagonal entropies after a quench with no pair structure

Bertini, Bruno; Tartaglia, Elena; Calabrese, Pasquale

doi:10.1088/1742-5468/aac73f

Cited by 60 publications

(80 citation statements)

References 95 publications

(215 reference statements)

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“…Although the entanglement evolution after a quench has been studied for many physical lattice models, both free [5,[7][8][9][10][11][12][13][14][15][16][17][18][19][20] and interacting [21][22][23][24], complete analytic derivations of such linear behaviour remained elusive so-far. In 1 + 1 dimensions, they are still based either on conformal field theory techniques [5,25] or conjectural large space-time asymptotics for block Töplitz matrices [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Entanglement dynamics after a quench in Ising field theory: a branch point twist field approach

Castro-Alvaredo

Lencsés

Szécsényi

et al. 2019

J. High Energ. Phys.

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We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m 0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the Rényi entropies at large times mt 1 emerges from a perturbative calculation at second order. We also show that the Rényi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt) −3/2 . The oscillatory terms are correctly predicted by an alternative perturbation series, in the prequench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points.

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Section: Introductionmentioning

confidence: 99%

Entanglement dynamics after a quench in Ising field theory: a branch point twist field approach

Castro-Alvaredo

Lencsés

Szécsényi

et al. 2019

J. High Energ. Phys.

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“…where χ A (x) is the characteristic function of the interval A, the function f α,λ (x) denotes the contribution to the entanglement of the pair (α, λ), (α, −λ), with rapidity ±λ and species α, originated at x, and X α,λ (x, t) gives the position at time t of the quasiparticle that was created at position x at time 0. This picture can be extended to the case where the initial state consists of more complicated multiplets of correlated particles [25,26]. For the sake of simplicity, however, here we stick to cases where only pairs are produced and, moreover, we assume that the pairs are composed by particles of the same species.…”

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confidence: 99%

Entanglement evolution and generalised hydrodynamics: interacting integrable systems

2019

Self Cite

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We investigate the dynamics of bipartite entanglement after the sudden junction of two leads in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with Generalised Hydrodynamics we derive an analytical prediction for the dynamics of the entanglement entropy between a finite subsystem and the rest. We find that the entanglement rate between the two leads depends only on the physics at the interface and differs from the rate of exchange of thermodynamic entropy. This contrasts with the behaviour in free or homogeneous interacting integrable systems, where the two rates coincide. ContentsRecent years witnessed interdisciplinary efforts aiming at understanding how statistical mechanics and thermodynamics arise from the out-of-equilibrium dynamics of isolated quantum many-body systems [1,2,3,4,5]. Characterising the entanglement spreading emerged as one of the key aspects to elucidate this issue [6]. The reason is twofold.First, the spreading of entanglement provides universal information on the time evolution of the system, removing most of the inessential details that are typically tied to the correlation functions of local observables. This is best illustrated by considering the evolution of bipartite entanglement in pure states, customarily measured by the entanglement entropy [6]. Under mild hypotheses, preparing the system in a low entangled state and switching on spatially local interactions, the entanglement entropy of a finite subsystem exhibits a linear increase at intermediate times, whereas it saturates at asymptotically large times. This behaviour is observed in a huge variety of physical systems, ranging from random unitary circuits to integrable models

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“…P 1 and P 2 are instantaneously displaced by a distance d 1,2 and d 2,1 (cf. (26)). The displacement of the particles is implemented with the procedures JUMPLEFT and JUMPRIGHT, which are described in Fig.…”

Section: Flea Gas For the Xxz Chain And Numerical Implementationmentioning

confidence: 99%

“…Here we restrict ourselves to the situation in which only entangled pairs are present. Other situations, for instance the case of entangled "triplets", have been considered, at least in free models [26,27].…”

Section: Introductionmentioning

confidence: 99%

Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

Mestyán

Alba

2020

SciPost Phys.

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We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb-Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the full-time dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available. arXiv:1905.03206v3 [cond-mat.stat-mech]

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Entanglement and diagonal entropies after a quench with no pair structure

Cited by 60 publications

References 95 publications

Entanglement dynamics after a quench in Ising field theory: a branch point twist field approach

Entanglement dynamics after a quench in Ising field theory: a branch point twist field approach

Entanglement evolution and generalised hydrodynamics: interacting integrable systems

Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

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