Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

Abstract

We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values, that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.

14 pages, 1 table, minor changes

References in corpus (25)

• Thermalization and its mechanism for generic isolated quantum systems
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Dephasing and the steady state in quantum many-particle systems
• Generalized Thermalization in an Integrable Lattice System
• Quantum quench dynamics of the Luttinger model
• Absence of Thermalization in Nonintegrable Systems
• Effective thermal dynamics following a quantum quench in a spin chain
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Dynamical Correlations after a Quantum Quench
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Time evolution of correlations in strongly interacting fermions after a quantum quench
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Dynamics in the Ising field theory after a quantum quench
• Hidden Grassmann structure in the XXZ model
• Quantum relaxation after a quench in systems with boundaries
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Luttinger liquid universality in the time evolution after an interaction quench
• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction
• Finite-size corrections vs. relaxation after a sudden quench
• Algebraic representation of correlation functions in integrable spin chains
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Global large time dynamics and the generalized Gibbs ensemble

Cited by in corpus (128)

• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Quantum quenches in 1+1 dimensional conformal field theories
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Quasilocal charges in integrable lattice systems
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Entanglement dynamics after quantum quenches in generic integrable systems
• "Light-cone" dynamics after quantum quenches in spin chains
• Prethermalization and thermalization in models with weak integrability breaking
• Prethermalization and universal dynamics in near-integrable quantum systems
• The Quench Action
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Analytic results for a quantum quench from free to hard-core one dimensional bosons
• Generalized Gibbs Ensembles for Quantum Field Theories
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• Quantum quench in the sine-Gordon model
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Interaction quenches in the 1D Bose gas
• On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
• From Interacting Particles to Equilibrium Statistical Ensembles
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Entanglement and quantum transport in integrable systems
• Determination of the Nonequilibrium Steady State Emerging from a Defect
• Quench action and Renyi entropies in integrable systems
• A Gaudin-like determinant for overlaps of Néel and XXZ Bethe states
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Thermalization and light cones in a model with weak integrability breaking
• Exact large-scale correlations in integrable systems out of equilibrium
• String-charge duality in integrable lattice models
• Integrable Floquet dynamics
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• Time-dependent generalized Gibbs ensembles in open quantum systems
• Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions
• Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• Quantum quenches from excited states in the Ising chain
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Quench Dynamics of the Anisotropic Heisenberg Model
• Entanglement spreading in non-equilibrium integrable systems
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
• Boundary State in an Integrable Quantum Field Theory Out of Equilibrium
• Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
• Quantum Quenches in the Luttinger model and its close relatives
• Néel-XXZ state overlaps: odd particle numbers and Lieb-Liniger scaling limit
• Pre-relaxation in weakly interacting models
• Pumping approximately integrable systems
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
• Exact solution for the quench dynamics of a nested integrable system
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Short distance correlators in the XXZ spin chain for arbitrary string distributions
• Stationary entanglement entropies following an interaction quench in 1D Bose gas
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Overlaps of $q$-raised Néel states with XXZ Bethe states and their relation to the Lieb-Liniger Bose gas
• How order melts after quantum quenches
• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• Entanglement revivals as a probe of scrambling in finite quantum systems
• Integrability-protected adiabatic reversibility in quantum spin chains
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• A short introduction to Generalized Hydrodynamics
• Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
• Quasi-local conserved charges and spin transport in spin-$1$ integrable chains
• Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems
• Interaction quench in a trapped one-dimensional Bose gas
• Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Quantum quench in long-range field theories
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• Excited state correlations of the finite Heisenberg chain
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• The quench action approach in finite integrable spin chains
• Rényi entropies of generic thermodynamic macrostates in integrable systems
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold
• Quantum Quench of the trap frequency in the harmonic Calogero model
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Integrable quenches in nested spin chains I: the exact steady states
• Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
• Quench dynamics of one-dimensional bosons in a commensurate periodic potential: A quantum kinetic equation approach
• Quench echo and work statistics in integrable quantum field theories
• Prethermalization at Low Temperature: the Scent of Long-Range Order
• Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• On Truncated Generalized Gibbs Ensembles in the Ising Field Theory
• Quantum quenches in the thermodynamic limit. II. Initial ground states
• Quenching the magnetic flux in 1d fermionic ring: Loschmidt echo and edge singularity
• Stationary state after a quench to the Lieb-Liniger from rotating BECs
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Engineering generalized Gibbs ensembles with trapped ions
• Superluminal moving defects in the Ising spin chain
• Lack of thermalization for integrability-breaking impurities
• Quenches from gaussian bosons to Tonks-Girardeau gas: stationary states and effects of a confining potential
• Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• Global Quenches after Localised Perturbations
• Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
• Charge-current correlation equalities for quantum systems far from equilibrium
• Correlation and entanglement spreading in nested spin chains
• Stationary ensemble approximations of dynamic quantum states: Optimizing the Generalized Gibbs Ensemble
• Soliton splitting in quenched classical integrable systems
• All local conserved quantities of the XXZ model
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Evolution of the magnetization after a local quench in the critical transverse-field Ising chain
• Strong Eigenstate Thermalization within a Generalized Shell in Noninteracting Integrable Systems
• Spin conductivity of the XXZ chain in the antiferromagnetic massive regime
• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz
• Exact many-body scars based on pairs or multimers in a chain of spinless fermions
• Critical quench dynamics of random quantum spin chains: Ultra-slow relaxation from initial order and delayed ordering from initial disorder
• Generalized thermalization for integrable system under quantum quench
• Entanglement Pre-thermalization in an Interaction Quench between Two Harmonic Oscillators
• Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains
• Long-lived non-thermal states in pumped one-dimensional systems of hard-core bosons
• Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach
• Generalized Gibbs Ensemble from Eigenstate Entanglement Hamiltonian