Relaxation dynamics in the gapped XXZ spin-1/2 chain

Abstract

We study the dynamics of a quench-prepared domain wall state released into a system whose unitary time evolution is dictated by the Hamiltonian of the Heisenberg spin-1/2 gapped antiferromagnetic chain. Using exact wavefunctions and their overlaps with the domain wall state allows us to describe the release dynamics to high accuracy, up to the long-time limit, for finite as well as infinite systems. The results for the infinite system allow us to rigorously prove that the system in the gapped regime ($\Delta >1$) cannot thermalize in the strict sense.

18 pages, 4 figures

References in corpus (33)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Time-dependence of correlation functions following a quantum quench
• Quantum Inverse Scattering Method and Correlation Functions
• Quantum Quenches in Extended Systems
• Dynamics of Loschmidt echoes and fidelity decay
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• The Luttinger model following a sudden interaction switch-on
• 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
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Strongly correlated fermions after a quantum quench
• Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
• Effective thermal dynamics following a quantum quench in a spin chain
• Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
• Quantum quenches and thermalization in one-dimensional fermionic systems
• Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
• 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
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Unitary equilibrations: probability distribution of the Loschmidt echo
• Quantum quenches from integrability: the fermionic pairing model
• Correlations in an expanding gas of hard-core bosons
• Bethe Ansatz approach to quench dynamics in the Richardson model
• Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
• Deformed strings in the Heisenberg model
• The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
• Edge-locking and quantum control in highly polarized spin chains

Cited by in corpus (95)

• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Time evolution of local observables after quenching to an integrable model
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Alternatives to Eigenstate Thermalization
• Reduced Density Matrix after a Quantum Quench
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Prethermalization and universal dynamics in near-integrable quantum systems
• The Quench Action
• What is an integrable quench?
• Microwave-engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms
• Generalized Gibbs Ensembles for Quantum Field Theories
• Inhomogeneous field theory inside the arctic circle
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Dynamics in the Ising field theory after a quantum quench
• Superdiffusion in spin chains
• Quantum Quenches in an XXZ Spin Chain from a Spatially Inhomogeneous Initial State
• Non-equilibrium steady states in the quantum XXZ spin chain
• Inhomogeneous quenches in a fermionic chain: exact results
• Initial state dependence of the quench dynamics in integrable quantum systems
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Luttinger liquid universality in the time evolution after an interaction quench
• Quench Dynamics in Randomly Generated Extended Quantum Models
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Entanglement spreading after a geometric quench in quantum spin chains
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: Complete relaxation of one-body observables
• Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Exact relaxation dynamics of a localized many-body state in the 1D bose gas
• Fate of Majorana fermions and Chern numbers after a quantum quench
• Emergent eigenstate solution to quantum dynamics far from equilibrium
• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
• Single-particle and many-body analyses of a quasiperiodic integrable system after a quench
• Finite-temperature magnetization transport of the one-dimensional anisotropic Heisenberg model
• Initial state dependence of the quench dynamics in integrable quantum systems. II. Thermal states
• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
• Domain wall dynamics in integrable and chaotic spin-1/2 chains
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• Geometric quenches in quantum integrable systems
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
• A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model
• Free fermions at the edge of interacting systems
• Initial state dependence of the quench dynamics in integrable quantum systems. III. Chaotic states
• Quantum quench in 1D: Coherent inhomogeneity amplification and 'supersolitons'
• Quantum quenches and work distributions in ultra-low-density systems
• One-dimensional Quantum Spin Dynamics of Bethe String States
• Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
• Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in an XXZ chain
• Quenched dynamics in interacting one-dimensional systems: Appearance of current carrying steady states from initial domain wall density profiles
• A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas
• Dynamics of thermalization and decoherence of a nanoscale system
• Edge mode dynamics of quenched topological wires
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Quasi-soliton scattering in quantum spin chains
• Universal Features of the Excitation Spectrum in Generalized Gibbs Distribution Ensemble
• Exactness of the mean-field dynamics in optical cavity systems
• Localized dynamics following a quantum quench in a non-integrable system: An example on the sawtooth ladder
• Bose-Hubbard ladder subject to effective magnetic field: quench dynamics in a harmonic trap
• Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process
• Recurrence time in the quantum dynamics of the 1D Bose gas
• Domain-wall melting in ultracold boson systems with holes and spin-flip defects
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Long time asymptotics of the totally asymmetric simple exclusion process
• A random phase approximation study of one-dimensional fermions after a quantum quench
• Domain wall melting in spin-1 chains
• Ground-state phase diagram for a system of interacting, $D(D_3)$ non-Abelian anyons
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• Growing Schrödinger's cat states by local unitary time evolution of product states
• Dynamics and thermalization in correlated one-dimensional lattice systems
• Spin dynamics in finite cyclic XY model
• Absence of thermalization of free systems coupled to gapped interacting reservoirs
• Interaction-induced transition in quantum many-body detection probability
• Exact quantum dynamics of yrast states in the finite 1D Bose gas
• Fractionalization Waves in Two-dimensional Dirac Fermions: Quantum Imprint from One Dimension
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Non-Equilibrium Steady State of the Lieb-Liniger model: multiple-integral representation of the time evolved many-body wave-function
• Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains
• Relaxation of antiferromagnetic order and growth of Rényi entropy in a generalized Heisenberg star
• A journey into localization, integrability and thermalization
• Slow transport and bound states for spinless fermions with long-range Coulomb interactions on one-dimensional lattices
• Entanglement, decoherence and thermal relaxation in exactly solvable models
• Entropy production and statistical relaxation of dipolar bosons and fermions in interaction quench dynamics
• Strong zero modes in integrable spin-S chains