Quench dynamics and relaxation in isolated integrable quantum spin chains

By F. Essler, M. Fagotti. 2016

573 citations recorded by the source corpus.

We review the dynamics after quantum quenches in integrable quantum spin chains. We give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the description of the steady state by (generalized) Gibbs ensembles. We then turn to general features in the time evolution of local observables after the quench, using a simple model of free fermions as an example. In the second part we present an overview of recent progress in describing quench dynamics in two key paradigms for quantum integrable models, the transverse field Ising chain and the anisotropic spin-1/2 Heisenberg chain.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/66c8e509d04b4e2a7bd69aa9c2f8d7fb4bb0bf2e

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In Atomic and Molecular Physics, and Optics

In Geometry and Topology

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Citations in the corpus

Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos (2018, unknown): “On the other hand, for h 1⁄4 0 the system is integrable, and finite subsystems relax to generalized Gibbs ensembles [71,72].”
Emergent hydrodynamics in integrable quantum systems out of equilibrium (2016, background): “(20) The potentials β can be recovered: the occupation number is related to the one-particle eigenvalue w(θ) =∑ i βihi(θ) of the charge ∑ i βiQi in the GGE (4) via the so-called pseudo-energy w(θ) [60, 61]: n(θ) = 1 1 + exp [ w(θ) ] (21) w(θ) = w(θ)− ∫ dγ 2π ϕ(θ − γ) log(1 + e− w(γ)).”
A note on generalized hydrodynamics: inhomogeneous fields and other concepts (2016, background): “In this context, entropy maximization is conjectured to generate states in the infinite-dimensional variety of so-called generalized Gibbs ensembles(1) (GGEs) [22, 23], which therefore are used to characterize fluid cells.”
Generalized Gibbs ensemble in integrable lattice models (2016, background): “More specifically, we focus on two paradigmatic integrable models that can be mapped onto noninteracting ones: hard-core bosons (XX model) and the transverse field Ising model (see also the review by Essler and Fagotti in this volume [70]).”
Entanglement in a fermion chain under continuous monitoring (2018, unknown): “[67] for a review on quench dynamics.”
Ergodicity breaking transition in finite disordered spin chains (2020, unknown): “[15] F.”
Simulating quantum many-body dynamics on a current digital quantum computer (2019, background): “Setup In this article we study global quantum quenches [56, 57], that is we calculate local observables and correlators of the form”
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “[19] Fabian H L Essler and Maurizio Fagotti, “Quench dynamics and relaxation in isolated integrable quantum spin chains,” Journal of Statistical Mechanics: Theory”
Conformal field theory out of equilibrium: a review (2016, background): “In these studies, an important concept is that of generalized Gibbs ensembles [10] (with a refinement based on pseudolocal charges [8, 11, 14, 15]): integrable models do not, generically, thermalize, but rather a generalized thermalization phenomenon occurs.”
Statistical localization: From strong fragmentation to strong edge modes (2019, background): “[16] Fabian H L Essler and Maurizio Fagotti, “Quench dynamics and relaxation in isolated integrable quantum spin chains,” Journal of Statistical Mechanics: Theory and Experiment 2016, 064002 (2016).”
Drude Weight for the Lieb-Liniger Bose Gas (2017, background): “(3.4) A generalized Gibbs ensemble (GGE) is specified by some density function f(v) independent of x. Microscopically this means that the hard rods have uniform density and independent velocities with probability density function ρ−1f(v).”
Prethermalization and Thermalization in Isolated Quantum Systems (2018, background): “By dephasing, observables quickly settle to quasisteady states that are well described by generalized Gibbs ensembles (GGEs) [16–20] of the noninteracting systems.”
Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws (2017, background): “This renewed interest has been driven by theoretical advances involving the long-sought demonstration that many-body localization (MBL) exists [1], as well as by the study of quantum information theory and integrable systems [2].”