Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain

Brockmann, Michael; Wouters, Bram; Fioretto, Davide; Nardis, Jacopo De; Vlijm, Rogier; Caux, Jean-Sébastien

doi:10.1088/1742-5468/2014/12/p12009

Cited by 98 publications

(189 citation statements)

References 120 publications

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“…The question of thermalization can then reduce to the question of how narrow in energy the overlap distribution is. Recent work (such as the "quench action" approach [82][83][84][85][86][87][88] and an approach based on linked-cluster expansions [89,90]) has formulated calculations of long-time expectation values directly in the thermodynamic limit, thus avoiding the explicit calculation of overlaps in finite-size systems.…”

Section: O(t) = ψ(T)|o|ψ(t) = ψmentioning

confidence: 99%

“…By taking the thermodynamic limit of the results of Ref. [122], it was possible to investigate the long-time limit in quenches to the antiferromagnetic gapped phase ∆ f > 1 [84][85][86] and also to the isotropic point ∆ f = 1 [86], using the quench action approach [82]. However, extracting all the overlaps for large but finite chains by means of the exact formulas of Refs.…”

Section: The Modelmentioning

confidence: 99%

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Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

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Section: O(t) = ψ(T)|o|ψ(t) = ψmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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“…The GGE is expected to describe the equilibration of local observables after a quantum quench in an integrable system by taking into account all constraints associated to its conserved charges [3,5,. While in its standard form it was constructed exclusively out of local conserved charges [28,29], it has been recently shown that quasi-local charges must also be included [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. This gives an answer to the fundamental question of how much information about the initial state survives in the final values of local observables.…”

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confidence: 99%

Memory-preserving equilibration after a quantum quench in a one-dimensional critical model

Sotiriadis

2016

Phys. Rev. A

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One of the fundamental principles of statistical physics is that only partial information about a system's state is required for its macroscopic description. This is not only true for thermal ensembles, but also for the unconventional ensemble, known as Generalized Gibbs Ensemble (GGE), that is expected to describe the relaxation of integrable systems after a quantum quench. By analytically studying the quench dynamics in a prototypical one-dimensional critical model, the massless free bosonic field theory, we find evidence of a novel type of equilibration characterized by the preservation of an enormous amount of memory of the initial state that is accessible by local measurements. In particular, we show that the equilibration retains memory of non-Gaussian initial correlations, in contrast to the case of massive free evolution which erases all such memory. The GGE in its standard form, being a Gaussian ensemble, fails to predict correctly the equilibrium values of local observables, unless the initial state is Gaussian itself. Our findings show that the equilibration of a broad class of quenches whose evolution is described by Luttinger liquid theory with an initial state that is non-Gaussian in terms of the bosonic field, is not correctly captured by the corresponding bosonic GGE, raising doubts about the validity of the latter in general onedimensional gapless integrable systems such as the Lieb-Liniger model. We also propose that the same experiment by which the GGE was recently observed [Langen et al., Science 348 (2015) 207-211] can also be used to observe its failure, simply by starting from a non-Gaussian initial state.Introduction -Understanding the physics of quantum many-body systems out of equilibrium is one of the most challenging open problems today [1,2]. Of central interest is the problem of quantum quenches i.e. abrupt changes of the Hamiltonian parameters of a closed quantum system [3], especially in one-dimensional (1d) integrable systems where the study of quantum dynamics has led to intriguing discoveries, like the experimental observation of lack of thermalization [4] and the theoretical prediction of the Generalized Gibbs Ensemble (GGE) [5] which has recently been observed experimentally [6]. The GGE is expected to describe the equilibration of local observables after a quantum quench in an integrable system by taking into account all constraints associated to its conserved charges [3,5,. While in its standard form it was constructed exclusively out of local conserved charges [28,29], it has been recently shown that quasi-local charges must also be included [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. This gives an answer to the fundamental question of how much information about the initial state survives in the final values of local observables. Other aspects of interest are the asymptotic behavior towards equilibrium [13,30,34,41,61] or the restoration of symmetries of the post-quench Hamiltonian that are absent in the initial state [62,63].

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“…the one reported in Fig. 1) in the GGE and for infinite time can be expanded close to the Δ = ∞ point obtaining [66] …”

Section: -P4mentioning

confidence: 84%

“…From these overlaps, the infinite time limit of the evolution has been explicitly calculated for the Neel state in Ref. [65,66] and for the dimer state in [67], again exploiting the representative state approach of Ref. [52].…”

Section: -P4mentioning

confidence: 99%

Non-equilibrium dynamics of isolated quantum systems

Calabrese

2015

EPJ Web of Conferences

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Abstract. The non-equilibrium dynamics of isolated quantum systems represent a theoretical and experimental challenge raising many fundamental questions with applications to different fields of modern physics. In these proceedings, we briefly review some of the recent findings on the subject, with particular emphasis to the existence of stationary expectation values of local observables and to their statistical mechanics description. It turns out that the appropriate statistical ensemble describing these asymptotic values depends on whether the Hamiltonian governing the time evolution is integrable or not.

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Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain

Cited by 98 publications

References 120 publications

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Memory-preserving equilibration after a quantum quench in a one-dimensional critical model

Non-equilibrium dynamics of isolated quantum systems

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