Quench dynamics and relaxation in isolated integrable quantum spin chains

Abstract

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 (gen- eralized) Gibbs ensembles. When 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.

48 pages, 10 figures; Review article for special issue of JSTAT on non-equilibrium dynamics in integrable systems; published version

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• Duality between weak and strong interactions in quantum gases
• Adiabatic gauge potential and integrability breaking with free fermions
• Quasiparticle Picture for Entanglement Hamiltonians in Higher Dimensions
• Thermalization of long range Ising model in different dynamical regimes: a full counting statistics approach
• Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
• Decay of long-lived oscillations after quantum quenches in gapped interacting quantum systems
• Continuum approach to real time dynamics of 1+1D gauge field theory: out of horizon correlations of the Schwinger model
• Self--averaging of random quantum dynamics
• Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
• Non-equilibration, synchronization, and time crystals in isotropic Heisenberg models
• $T\overline{T}$ deformations and the width of fundamental particles
• Steady off-diagonal long-range order state in a half-filled dimerized Hubbard chain induced by a resonant pulsed field
• Quantum heat waves in a one-dimensional condensate
• Quantum reaction-limited reaction-diffusion dynamics of noninteracting Bose gases
• Localization and integrability breaking in weakly interacting Floquet circuits
• Generalized thermalization for integrable system under quantum quench
• The Adiabatically Deformed Ensemble: Engineering Non-Thermal States of Matter
• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• Charging a Dimerized Quantum XY Chain
• The Staircase Model: Massless Flows and Hydrodynamics
• Quench dynamics of Rényi negativities and the quasiparticle picture
• Quantum jamming brings quantum mechanics to macroscopic scales
• The relevant excitations for the one-body function in the Lieb-Liniger model
• Quenching the Kitaev honeycomb model
• Structure of the Hamiltonian of mean force
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• Probing chaos in the spherical p-spin glass model
• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• Quasi-conserved quantities in the perturbed XXX spin chain
• Exploring Disordered Quantum Spin Models with a Multi-Layer Multi-Configurational Approach
• Hidden quasi-local charges and Gibbs ensemble in a Lindblad system
• Out-of-equilibrium full counting statistics in Gaussian theories of quantum magnets
• Integrability of Goldilocks quantum cellular automata
• Quantum quench in a driven Ising chain
• Generalized hydrodynamics of integrable quantum circuits
• Long-time equilibration can determine transient thermality
• The LeClair-Mussardo series and nested Bethe Ansatz
• The topological Kondo model out of equilibrium
• Prethermalization of light and matter in cavity-coupled Rydberg arrays
• Accuracy of time-dependent GGE under weak dissipation
• The second law of thermodynamics from concavity of energy eigenvalues
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Continuous-time quantum optimisation without the adiabatic principle
• Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids
• Duality defect in a deformed transverse-field Ising model
• General interaction quenches in a Luttinger liquid
• Non-Markovianity of subsystem dynamics in isolated quantum many-body systems
• Post quench entropy growth in a chiral clock model
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system
• Fragility to quantum fluctuations of classical Hamiltonian period doubling
• Emergent eigenstate solution for generalized thermalization
• Probing Off-diagonal Eigenstate Thermalization with Tensor Networks
• Generalized Gibbs ensembles in weakly interacting dissipative systems and digital quantum computers
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization
• Entanglement Propagation in Integrable Heisenberg Chains from a New Lens
• Symmetry-prohibited thermalization after a quantum quench
• Allosteric impurity effects in long spin chains
• Simulating spin dynamics with quantum computers
• Localized Fock Space Cages in Kinetically Constrained Models
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
• Non-stationarity and Dissipative Time Crystals: Spectral Properties and Finite-Size Effects
• The Hilbert-space structure of free fermions in disguise
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• Influence functional of many-body systems: temporal entanglement and matrix-product state representation
• Finite temperature single-particle Green's function in the Lieb-Liniger model
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Out-of-equilibrium Eigenstate Thermalization Hypothesis
• Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit
• Dynamical deconfinement transition driven by density of excitations
• Kinetics of Quantum Reaction-Diffusion systems
• The Yang-Baxter paradox
• Thermalization/Relaxation in integrable and free field theories: an Operator Thermalization Hypothesis
• Ab-Initio Approach to Many-Body Quantum Spin Dynamics
• Thermalization in a simple spin-chain model
• Reaction-diffusion dynamics of the weakly dissipative Fermi gas
• Observation of a generalized Gibbs ensemble in photonics
• Equilibration of quantum cat states
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Critical quantum dynamics of observables at eigenstate transitions
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• Quench-Probe Setup as Analyzer of Fractionalized Entanglement Spreading
• Generalised Hydrodynamics of Particle Creation and Decay
• Quench dynamics of negativity Hamiltonians
• A hydrodynamic approach to Stark localization
• Probing Hilbert space fragmentation using controlled dephasing
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Long-lived non-thermal states in pumped one-dimensional systems of hard-core bosons
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
• On computing non-equilibrium dynamics following a quench
• Predictive complexity of quantum subsystems
• Thermodynamic symmetry resolved entanglement entropies in integrable systems
• Ballistic Entanglement Cloud after a Boundary Quench
• Finite time path field theory perturbative methods for local quantum spin chain quenches
• Tensor Product Structure Geometry under Unitary Channels
• Ballistic propagation of a local impact in the one-dimensional $XY$ model
• Probing the many-body localized spin-glass phase through quench dynamics
• Universal efficiency boost in prethermal quantum heat engines at negative temperature
• Tails of Instability and Decay: a Hydrodynamic Perspective
• Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra
• 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
• Finite time path field theory and a new type of universal quantum spin chain quench behavior
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles
• Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices
• Quantum local random networks and the statistical robustness of quantum scars
• Time reversal symmetry protected chaotic fixed point in the quench dynamics of a topological $p$-wave superfluid
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect
• The second law of thermodynamics from concave energy in classical mechanics
• Rationally independent free fermions with local hopping
• Basis dependence of eigenstate thermalization
• Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States
• Vanishing correlations in stochastic and bistochastic controlled circuits
• Operator delocalization in disordered spin chains via exact MPO marginals
• Mediated interactions beyond the nearest neighbor in an array of superconducting qubits
• Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
• Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices
• Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
• Effects of intertube dipole-dipole interactions in nearly integrable one-dimensional ${}^{162}$Dy gases
• Theoretical study on thermalization in isolated quantum systems
• Nonlocal pseudospin dynamics in a quantum Ising chain
• Absence of local conserved charges of the Fredkin spin chain and its truncated versions
• Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State
• Generalised Gibbs Ensemble for spherically constrained harmonic models
• Bistabilities and domain walls in weakly open quantum systems
• Designing non-equilibrium states of quantum matter through stochastic resetting
• Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach
• Temperature and conditions for thermalization after canonical quenches
• Absence of thermalization after a local quench and strong violation of the eigenstate thermalization hypothesis