Thermalization and prethermalization in isolated quantum systems: a theoretical overview

Abstract

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal system to study the nonequilibrium dynamics in isolated quantum systems, triggering intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation in relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.

108 pages, 7 figures. Topical Review, to appear in J. Phys. B

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• Relaxation to Gaussian Generalized Gibbs Ensembles in Quadratic Bosonic Systems in the Thermodynamic Limit
• Ensemble dependence of information-theoretic contributions to the entropy production
• Bounding the finite-size error of quantum many-body dynamics simulations
• Nonequilibrium steady states of Bose-Einstein condensates with a local particle loss in double potential barriers
• Non-thermal dynamics in a spin-1/2 lattice Schwinger model
• Quantum supremacy in driven quantum many-body systems
• Discrete time-crystals in unbounded potentials
• Floquet States
• Non-thermal eigenstates and slow relaxation in quantum Fredkin spin chains
• A remark on the notion of independence of quantum integrals of motion in the thermodynamic limit
• Extreme many-body scarring in a quantum spin chain via weak dynamical constraints
• Modelling equilibration of local many-body quantum systems by random graph ensembles
• Metastable order protected by destructive many-body interference
• Robustness and eventual slow decay of bound states of interacting microwave photons in the Google Quantum AI experiment
• Thermal state entanglement entropy on a quantum graph
• Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems
• Universal defects statistics with strong long-range interactions
• Edge state, bound state and anomalous dynamics in the Aubry-André-Haper system coupled to non-Markovian baths
• Tensor-network approach to thermalization in open quantum many-body systems
• Adiabatic time evolution of highly excited states
• Back-reaction and correlation effects on pre-thermalization in Mott-Hubbard systems
• Structure of the Hamiltonian of mean force
• Site-selective doublon-holon dynamics in a pumped one-dimensional Hubbard superlattice with staggered Coulomb interactions
• The effect of dressing on thermalization of interacting waves
• Breakdown of Measurement-Induced Phase Transitions Under Information Loss
• Dilution of error in digital Hamiltonian simulation
• Quantum Fragmentation in the Extended Quantum Breakdown Model
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Open-system eigenstate thermalization in a noninteracting integrable model
• Tangent space generators of matrix product states and exact Floquet quantum scars
• Trapping Hard-Core Bosons in Flatband Lattices
• Canonical density matrices from eigenstates of mixed systems
• Finite temperature detection of quantum critical points via internal quantum teleportation
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• Photoinduced prethermalization phenomena in correlated metals
• Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems
• Long-time equilibration can determine transient thermality
• Single-quasiparticle eigenstate thermalization
• Quantum memory at an eigenstate phase transition in a weakly chaotic model
• Universal scaling at a pre-thermal dark state
• Vortex loop dynamics and dynamical quantum phase transitions in 3D fermion matter
• The missing quantum number of the Floquet states
• Quantum many-body scars in the Bose-Hubbard model with a three-body constraint
• Exotic signature of dynamical quantum phase transition in the time evolution of engineered initial state
• Dynamical phase transitions of information flow in random quantum circuits
• Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry
• Closeness of the reduced density matrix of an interacting small system to the Gibbs state
• Quasi-conserved quantities in the perturbed XXX spin chain
• Exact spectral form factors of non-interacting fermions with Dyson statistics
• Counting atypical black hole microstates from entanglement wedges
• Dynamical quantum phase transitions from random matrix theory
• Key Observable for Linear Thermalization
• Relaxation time as a control parameter for exploring dynamical phase diagrams
• Quantum coherence assisted dynamical phase transition
• On the role of the Integrable Toda model in one-dimensional molecular dynamics
• Screening the Coulomb interaction leads to a prethermal regime in two-dimensional bad conductors
• Phase Crossover induced by Dynamical Many Body Localization in Periodically Driven Long-Range Spin Systems
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• Subsystem eigenstate thermalization hypothesis for translation invariant systems
• Nontrivial damping of quantum many-body dynamics
• Prethermalization in the PXP Model under Continuous Quasiperiodic Driving
• Duality defect in a deformed transverse-field Ising model
• A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
• Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
• Non-Markovianity of subsystem dynamics in isolated quantum many-body systems
• Floquet theory and applications in open quantum and classical systems
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Low-energy prethermal phase and crossover to thermalization in nonlinear kicked rotors
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Prethermalization of quantum systems interacting with non-equilibrium environments
• Discrete Time Crystal Phase of Higher Dimensional Integrable Models
• Emergent eigenstate solution for generalized thermalization
• Engineering subharmonic responses beyond prethermalization via Floquet scar states
• Quantum Joule Expansion of One-Dimensional Systems
• Autonomous Stabilization of Floquet States Using Static Dissipation
• General theory for discrete symmetry-breaking equilibrium states
• Floquet analysis of time-averaged trapping potentials
• Macroscopic Thermalization for Highly Degenerate Hamiltonians After Slight Perturbation
• Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving
• Symmetry-prohibited thermalization after a quantum quench
• Anomalous Diffusion, Prethermalization, and Particle Binding in an Interacting Flat Band System
• New equilibrium ensembles for isolated quantum systems
• Probing Off-diagonal Eigenstate Thermalization with Tensor Networks
• Many-Body Localization in Translational Invariant Diamond Ladders with Flat Bands
• A New Era of Quantum Materials Mastery and Quantum Simulators In and Out of Equilibrium
• Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach
• One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results
• Scaling theory of fading ergodicity
• Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos
• Allosteric impurity effects in long spin chains
• Systematic construction of asymptotic quantum many-body scar states and their relation to supersymmetric quantum mechanics
• Trends of information backflow in disordered spin chains
• Subexponential decay of local correlations from diffusion-limited dephasing
• Strong Markov dissipation in driven-dissipative quantum systems
• Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics
• Typical perturbation theory: conditions, accuracy and comparison with a mesoscopic case
• Dynamical dimerization phase in Jaynes-Cummings lattices
• Enhanced localization in the prethermal regime of continuously measured many-body localized systems
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Ergodicity breaking transition in zero dimensions
• Persistent many-body quantum echoes
• Prethermalization of density-density correlations after an interaction quench in the Hubbard model
• Dynamical phase transition of light in time-varying nonlinear dispersive media
• Signatures of many-body localization and metastability by weak perturbation
• Absence of nontrivial local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions
• Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems
• Critical quantum dynamics of observables at eigenstate transitions
• Time evolution of the local density of states of strongly correlated fermions coupled to a nanoprobe
• Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Prethermalization for Deformed Wigner Matrices
• Thermalization in a simple spin-chain model
• Thermalization of isolated quantum many-body system and the role of entanglement
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Smooth Crossover Between Weak and Strong Thermalization using Rigorous Bounds on Equilibration of Isolated Systems
• Time crystal embodies chimeralike state in periodically driven quantum spin system
• Taking the temperature of quantum many-body scars
• Delocalization in a partially disordered interacting many-body system
• Dynamical control in a prethermalized molecular ultracold plasma: Local dissipation drives global relaxation
• Tensor Product Structure Geometry under Unitary Channels
• Robustness of near-thermal dynamics on digital quantum computers
• Nonequilibrium phase transition in a driven-dissipative quantum antiferromagnet
• Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction
• Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction
• Robustness of quantum symmetries against perturbations
• Long-Time Behavior of Typical Pure States from Thermal Equilibrium Ensembles
• Spatial correlations and entanglement in a hybrid system of N fermion pairs with harmonic interaction
• Dynamics in the presence of local symmetry-breaking impurities
• Clausius' theorem and the Second law in the process of isoenergetic thermalization
• Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory
• Quantum thermalization and average entropy of a subsystem
• Emergent Viscous Hydrodynamics From a Single Quantum Particle
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States
• Random initial data and average shock time in the Fermi-Pasta-Ulam-Tsingou chain
• Dynamics and steady states of tight-binding chains in presence of isolated defects
• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
• Teleportation based detection of quantum critical points using small spin chains
• Sample complexity of matrix product states at finite temperature
• Exploiting many-body localization for scalable variational quantum simulation
• Anomalous Landau damping and algebraic thermalization in two-dimensional superfluids far from equilibrium
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Emergence of prethermal time quasicrystalline order in a quasiperiodically driven non-interacting spin chain
• Observation of hierarchy of Hilbert space ergodicities in the quantum dynamics of a single spin
• Basis dependence of eigenstate thermalization
• Entropy production and statistical relaxation of dipolar bosons and fermions in interaction quench dynamics
• Absence of thermalization after a local quench and strong violation of the eigenstate thermalization hypothesis
• Tunable Hilbert space fragmentation and extended critical regime
• Does the Eigenstate Thermalization Hypothesis Imply Thermalization?
• Temperature and conditions for thermalization after canonical quenches
• Testing eigenstate decoherence hypothesis in a model of collisional decoherence
• Finding periodic orbits in projected quantum many-body dynamics
• Necessity of entanglement for the typicality argument in statistical mechanics
• Relaxation mechanisms in a disordered system with the Poisson level statistics
• Counterdiabatic driving for periodically driven open quantum systems
• Error bounds on the universal Lindblad equation in the thermodynamic limit
• Hydrodynamic model of skyrmions and vorticities in the spin-1 Bose-Einstein condensate in ferromagnetic phase at finite temperatures
• Controlling discrete time crystals via single-site operations in zero-field diamond quantum simulators
• Persistent-current states originating from the Hilbert space fragmentation in momentum space
• Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges
• Pure states statistical mechanics: On its foundations and applications to quantum gravity
• Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential
• Statistical Floquet prethermalization of the Bose-Hubbard model
• Quasi-adiabatic thermal ensemble preparation in the thermodynamic limit
• Engineering micromotion in Floquet prethermalization via space-time symmetries
• Effects of intertube dipole-dipole interactions in nearly integrable one-dimensional ${}^{162}$Dy gases
• Nonergodic delocalized paramagnetic states in quantum neural networks
• Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses
• Edge States Effects in Quantum Work Statistics
• Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir
• A Note on the Eigenstate Thermalization Hypothesis