Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems

Abstract

A quantum many-body system which is prepared in the ground state of an integrable Hamiltonian does not directly thermalize after a sudden small parameter quench away from integrability. Rather, it will be trapped in a prethermalized state and can thermalize only at a later stage. We discuss several examples for which this prethermalized state shares some properties with the nonthermal steady state that emerges in the corresponding integrable system. These examples support the notion that nonthermal steady states in integrable systems may be viewed as prethermalized states that never decay further. Furthermore we show that prethermalization plateaus are under certain conditions correctly predicted by generalized Gibbs ensembles, which are the appropriate extension of standard statistical mechanics in the presence of many constants of motion. This establishes that the relaxation behaviors of integrable and nearly integrable systems are continuously connected and described by the same statistical theory.

11 pages, 2 figures

References in corpus (38)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• The many-body localization phase transition
• Many body localization in Heisenberg XXZ magnet in a random field
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• The Luttinger model following a sudden interaction switch-on
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• Generalized Thermalization in an Integrable Lattice System
• Quench dynamics across quantum critical points
• Strongly correlated fermions after a quantum quench
• Quantum quench dynamics of the Luttinger model
• Typicality for Generalized Microcanonical Ensembles
• Remarks on the notion of quantum integrability
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Effective thermal dynamics following a quantum quench in a spin chain
• Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
• Quantum Quenches, Thermalization and Many-Body Localization
• Quantum chaos and thermalization in gapped systems
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Metastable superfluidity of repulsive fermionic atoms in optical lattices
• Correlations in an expanding gas of hard-core bosons
• Theory of time-resolved optical spectroscopy on correlated electron systems
• Thermal equilibration between two quantum systems
• New theoretical approaches for correlated systems in nonequilibrium
• Measuring correlated electron dynamics with time-resolved photoemission spectroscopy
• Dynamics of thermalisation in small Hubbard-model systems
• Relaxation dynamics of an exactly solvable electron-phonon model

Cited by in corpus (222)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Quantum Thermodynamics
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Nonequilibrium dynamical mean-field theory and its applications
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Experimental Observation of a Generalized Gibbs Ensemble
• Finite-temperature transport in one-dimensional quantum lattice models
• Dipolar physics: A review of experiments with magnetic quantum gases
• Quantum quenches in 1+1 dimensional conformal field theories
• Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
• Quasilocal charges in integrable lattice systems
• Ultracold atoms out of equilibrium
• Geometry and non-adiabatic response in quantum and classical systems
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Finite-size scaling of eigenstate thermalization
• Signatures of integrability in the dynamics of Rydberg-blockaded chains
• Prethermalization and thermalization in models with weak integrability breaking
• Quantum quench dynamics
• Thermalization near integrability in a dipolar quantum Newton's cradle
• Prethermalization and universal dynamics in near-integrable quantum systems
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Generalized Gibbs Ensembles for Quantum Field Theories
• Pre-thermalization in a non-integrable quantum spin chain after a quench
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• First order dynamical phase transitions
• Thermodynamics of quantum systems with multiple conserved quantities
• Infinite-time Average of Local Fields in an Integrable Quantum Field Theory after a Quantum Quench
• Prethermalization and Thermalization in Isolated Quantum Systems
• Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model
• Interaction quenches in the 1D Bose gas
• On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
• Quantum Quenches in the Thermodynamic Limit
• Thermodynamic resource theories, non-commutativity and maximum entropy principles
• Hydrodynamic long-time tails after a quantum quench
• The isolated Heisenberg magnet as a quantum time crystal
• From Interacting Particles to Equilibrium Statistical Ensembles
• Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Thermodynamic Equilibrium as a Symmetry of the Schwinger-Keldysh Action
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Determination of the Nonequilibrium Steady State Emerging from a Defect
• Thermalization and light cones in a model with weak integrability breaking
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions
• Hamiltonian truncation approach to quenches in the Ising field theory
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains
• Stroboscopic prethermalization in weakly interacting periodically driven systems
• Relaxation, pre-thermalization and diffusion in a noisy Quantum Ising Chain
• Aging and coarsening in isolated quantum systems after a quench: exact results for the quantum $O(N)$ model with $N\to \infty$
• Time-dependent generalized Gibbs ensembles in open quantum systems
• Creating quantum many-body scars through topological pumping of a 1D dipolar gas
• Prethermal Strong Zero Modes and Topological Qubits
• Exploring dynamical phase transitions and prethermalization with quantum noise of excitations
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Quantum quenches in the sine--Gordon model: a semiclassical approach
• Equilibration Properties of Classical Integrable Field Theories
• Multimode dynamics and emergence of a characteristic length-scale in a one-dimensional quantum system
• Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
• Statistics of the work done by splitting a one-dimensional quasi-condensate
• Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model
• Quantum Quench and Prethermalization Dynamics in A Two-Dimensional Fermi Gas with Long-range Interactions
• Quantum Quenches in the Luttinger model and its close relatives
• Work distribution and edge singularities for generic time-dependent protocols in extended systems
• Thermalization and dissipation in out of equilibrium quantum systems: A perturbative renormalization group approach
• Pre-relaxation in weakly interacting models
• Pumping approximately integrable systems
• Emergent eigenstate solution to quantum dynamics far from equilibrium
• Local relaxation and light-cone-like propagation of correlations in a trapped one-dimensional Bose gas
• Aperiodically driven integrable systems and their emergent steady states
• Symmetries and conserved quantities of boundary time crystals in generalized spin models
• Local and Quasilocal Conserved Quantities in Integrable Systems
• Breakdown of the generalized Gibbs ensemble for current-generating quenches
• Exact solution for the quench dynamics of a nested integrable system
• Area law violation for the mutual information in a nonequilibrium steady state
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems
• Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Non-Equilibrium Dynamics of a Noisy Quantum Ising Chain: statistics of the work and prethermalization after a sudden quench of the transverse field
• Initial state dependence of the quench dynamics in integrable quantum systems. II. Thermal states
• Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models
• Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in $d$ spatial dimensions
• Universal scaling at non-thermal fixed points of a two-component Bose gas
• Thermalisation of Local Observables in Small Hubbard Lattices
• Quench dynamics of the Ising field theory in a magnetic field
• Holographic Relaxation of Finite Size Isolated Quantum Systems
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction
• Quantum quench in long-range field theories
• Truncating the memory time in nonequilibrium DMFT calculations
• Typicality of Prethermalization
• Thermalization without eigenstate thermalization hypothesis after a quantum quench
• Integrable Mott insulators driven by finite electric field
• Quantum quenches in two spatial dimensions using chain array matrix product states
• Weak integrability breaking perturbations of integrable models
• Prethermalization and dynamical transition in an isolated trapped ion spin chain
• Non-thermal melting of Neel order in the Hubbard model
• Motion of a distinguishable impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking
• Nonequilibrium dynamical cluster theory
• Prethermalization and Thermalization of a Quenched Interacting Luttinger Liquid
• Prethermalization in the transverse-field Ising chain with long-range interactions
• Universal post-quench coarsening and quantum aging at a quantum critical point
• Entanglement prethermalization: Locally thermal but non-locally non-thermal states in a one-dimensional Bose gas
• Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
• Prethermalization at Low Temperature: the Scent of Long-Range Order
• Steady states of a quasiperiodically driven integrable system
• Interaction quenches in the two-dimensional fermionic Hubbard model
• Thermalization of a quantum Newton's cradle in a one-dimensional quasicondensate
• Prethermalization from a low-density Holstein-Primakoff expansion
• $Large-scale$ thermalization, prethermalization and impact of the temperature in the quench dynamics of two unequal Luttinger liquids
• Doublon formation by ions impacting a strongly correlated finite lattice system
• Local conservation laws in spin-1/2 XY chains with open boundary conditions
• Many-body localization and thermalization in the full probability distribution function of observables
• Photo-induced nonequilibrium states in Mott insulators
• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
• A quantum Boltzmann equation for strongly correlated electrons
• Prethermalisation and Thermalisation in the Entanglement Dynamics
• Dynamics of thermalization and decoherence of a nanoscale system
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Nonequilibrium Steady States and Resonant Tunneling in Time-Periodically Driven Systems with Interactions
• Relaxation of a classical spin coupled to a strongly correlated electron system
• Inflationary quasiparticle creation and thermalization dynamics in coupled Bose-Einstein condensates
• Quench dynamics of one-dimensional interacting bosons in a disordered potential: Elastic dephasing and critical speeding-up of thermalization
• Nonequilibrium current-carrying steady states in the anisotropic $XY$ spin chain
• Auxiliary Hamiltonian representation of the nonequilibrium Dyson equation
• Quasi-conserved charges in the perturbed spin-1/2 XXX model
• Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems
• Eigenvalue statistics of reduced density matrix during driving and relaxation
• Ion Impact Induced Ultrafast Electron Dynamics in Correlated Materials and Finite Graphene Clusters
• Equilibration and GGE in interacting-to-free Quantum Quenches in dimensions d>1
• Remnants of Anderson localization in pre-thermalization induced by white noise
• Engineering generalized Gibbs ensembles with trapped ions
• Non-equilibrium pre-thermal states in a two-dimensional photon fluid
• Lack of thermalization for integrability-breaking impurities
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Non equilibrium dynamics of isolated disordered systems: the classical Hamiltonian p-spin model
• Geometry of quantum observables and thermodynamics of small systems
• Disorder-free localization in quantum walks
• Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
• Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality
• Dynamics following a linear ramps in the $O(N)$ model: dynamical transition and statistics of excitations
• Quantum quenches, linear response and superfluidity out of equilibrium
• Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements
• Typicality of nonequilibrium (quasi-)steady currents
• Fluctuation Theorems and the Generalised Gibbs Ensemble in Integrable Systems
• Lehmann representation of the nonequilibrium self-energy
• Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model
• Suppression and Control of Pre-thermalization in Multi-component Fermi Gases Following a Quantum Quench
• Environment induced pre-thermalization in the Mott-Hubbard model
• Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems
• Thermalization Dynamics of Two Correlated Bosonic Quantum Wires After a Split
• Thermalization and prethermalization in the soft-wall AdS/QCD model
• Accelerated gap collapse in a Slater antiferromagnet
• Quench-induced dynamical phase transitions and $\pi$-synchronization in the Bose-Hubbard Model
• Entanglement prethermalization in the Tomonaga-Luttinger model
• Integrability breaking in the Rule 54 cellular automaton
• Geometric squeezing of rotating quantum gases into the lowest Landau level
• Extended dynamic Mott-transition in the two-band Hubbard model out of equilibrium
• Multiple relaxation times in perturbed XXZ chain
• The effect of optical lattice heating on the momentum distribution of a 1D Bose gas
• Long-living prethermalization in nearly integrable spin ladders
• Comparison of the Iterated Equation of Motion Approach and the Density Matrix Formalism for the Quantum Rabi Model
• Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate
• Quench Dynamics in Two-Dimensional Integrable SUSY Models
• Exploring integrability-chaos transition with a sequence of independent perturbations
• Hierarchy of double-time correlations
• Excitations in the Yang-Gaudin Bose gas
• Splitting a critical spin chain
• Peltier effect in strongly driven quantum wires
• Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
• Constrained thermalisation and topological superconductivity
• Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model
• Thermalization of isolated Bose-Einstein condensates by dynamical heat bath generation
• Back-reaction and correlation effects on pre-thermalization in Mott-Hubbard systems
• Metropolis-Hastings thermal state sampling for numerical simulations of Bose-Einstein condensates
• Relaxation dynamics of ultracold bosons in a double-well potential: Thermalization and prethermalization in a nearly integrable model
• Prethermalization and conservation laws in quasi-periodically-driven quantum systems
• Prethermalization in coupled one-dimensional quantum gases
• Approach to Equilibrium of a Nondegenerate Quantum System: Decay of Oscillations and Detailed Balance as Separate Effects of a Reservoir
• Planar quantum quenches: Computation of exact time-dependent correlation functions at large $N$
• Vanishing and non-vanishing persistent currents of various conserved quantities
• Prethermalization of light and matter in cavity-coupled Rydberg arrays
• Dynamical emergence of a Kosterlitz-Thouless transition in a disordered Bose gas following a quench
• Prethermalization with negative specific heat
• Loading and detecting a three-dimensional Fermi gas in one-dimensional optical superlattice
• Quasi-conserved quantities in the perturbed XXX spin chain
• Total Energy Dynamics and Asymptotics of the Momentum Distribution Following an Interaction Quench in a Two-component Fermi Gas
• Study of Open Systems with Molecules in Isotropic Liquids
• Key Observable for Linear Thermalization
• Energy and particle currents in a driven integrable system
• Low-energy prethermal phase and crossover to thermalization in nonlinear kicked rotors
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Prethermalization of quantum systems interacting with non-equilibrium environments
• Duality defect in a deformed transverse-field Ising model
• Generalized hydrodynamics in complete box-ball system for $U_q({\widehat{sl}}_n)$
• Quasiballistic transport in long-range anisotropic Heisenberg model
• Reversal of relaxation due to dephasing environment
• Finding local integrals of motion in quantum lattice models in the thermodynamic limit
• Time-dependent Mott transition in the periodic Anderson model with nonlocal hybridization
• Thermalization of a Dimerized Antiferromagnetic Spin Chain
• Efficient heat-energy conversion from a non-thermal Tomonaga-Luttinger liquid
• Small quenches and thermalization
• Prerelaxation in quantum, classical, and quantum-classical two-impurity models
• Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains
• Prethermalization of density-density correlations after an interaction quench in the Hubbard model
• Prethermalization for Deformed Wigner Matrices
• Disorder Enhanced Thermalization in Interacting Many-Particle System
• Dynamics of the Bose-Hubbard Chain for Weak Interactions
• Quantum chaos in a harmonic waveguide with scatterers
• Dynamics in the presence of local symmetry-breaking impurities
• Long-lived non-thermal states in pumped one-dimensional systems of hard-core bosons
• Scale invariant distribution functions in quantum systems with few degrees of freedom
• Anomalous Landau damping and algebraic thermalization in two-dimensional superfluids far from equilibrium
• Coherent heat exchange in a prethermalizing open quantum system
• A light-induced charge order mode in a metastable cuprate ladder
• Stabilizing open photon condensates by ghost-attractor dynamics
• Theoretical study on thermalization in isolated quantum systems
• Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system
• Thermalization of dipole oscillations in confined systems by rare collisions
• Tunable Hilbert space fragmentation and extended critical regime