Exact steady states for quantum quenches in integrable Heisenberg spin chains

Abstract

The study of quantum quenches in integrable systems has significantly advanced with the introduction of the Quench Action method, a versatile analytical approach to non-equilibrium dynamics. However, its application is limited to those cases where the overlaps between the initial state and the eigenstates of the Hamiltonian governing the time evolution are known exactly. Conversely, in this work we consider physically interesting initial states for which such overlaps are still unknown. In particular, we focus on different classes of product states in spin-$1/2$ and spin-$1$ integrable chains, such as tilted ferromagnets and antiferromagnets. We get around the missing overlaps by following a recent approach based on the knowledge of complete sets of quasi-local charges. This allows us to provide a closed-form analytical characterization of the effective stationary state reached at long times after the quench, through the Bethe ansatz distributions of particles and holes. We compute the asymptotic value of local correlations and check our predictions against numerical data.

25 pages, 11 figures; v2: minor revision and appendix added

References in corpus (41)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Quantum Quench in the Transverse Field Ising Chain
• Generalized Gibbs ensemble in integrable lattice models
• Experimental Observation of a Generalized Gibbs Ensemble
• The Luttinger model following a sudden interaction switch-on
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• 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
• "Light-cone" dynamics after quantum quenches in spin chains
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Generalized Gibbs Ensembles for Quantum Field Theories
• The dynamics and prethermalization of one dimensional quantum systems probed through the full distributions of quantum noise
• Quantum quench in the sine-Gordon model
• Quantum Quench from a Thermal Initial State
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quantum quenches from integrability: the fermionic pairing model
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Exactly conserved quasilocal operators for the XXZ spin chain
• Pre-relaxation in weakly interacting models
• Breakdown of the generalized Gibbs ensemble for current-generating quenches
• Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
• Short distance correlators in the XXZ spin chain for arbitrary string distributions
• Deformed strings in the Heisenberg model
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Prethermalization in one-dimensional Bose gases: description by a stochastic Ornstein-Uhlenbeck process
• Interaction quench in a trapped one-dimensional Bose gas
• Geometric quenches in quantum integrable systems
• Real-time dynamics in a strongly interacting bosonic hopping model: Global quenches and mapping to the XX chain
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature

Cited by in corpus (69)

• Entanglement and thermodynamics after a quantum quench in integrable systems
• Entanglement dynamics after quantum quenches in generic integrable systems
• What is an integrable quench?
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Entanglement asymmetry as a probe of symmetry breaking
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• The isolated Heisenberg magnet as a quantum time crystal
• From Interacting Particles to Equilibrium Statistical Ensembles
• Entanglement and quantum transport in integrable systems
• Quench action and Renyi entropies in integrable systems
• Thermalization and light cones in a model with weak integrability breaking
• Entanglement asymmetry and quantum Mpemba effect in the XY spin chain
• Time-dependent generalized Gibbs ensembles in open quantum systems
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Full Counting Statistics in the Transverse Field Ising Chain
• Entanglement spreading in non-equilibrium integrable systems
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Exact solution for the quench dynamics of a nested integrable system
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• 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
• Time evolution of the Luttinger model with nonuniform temperature profile
• Generalized Deep Thermalization for Free Fermions
• Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Low-Temperature Transport in Out-of-Equilibrium XXZ Chains
• Rényi entropies of generic thermodynamic macrostates in integrable systems
• Overlaps with arbitrary two-site states in the XXZ spin chain
• Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
• Integrable quenches in nested spin chains I: the exact steady states
• Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
• Current fluctuations in boundary-driven quantum spin chains
• Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas
• On Truncated Generalized Gibbs Ensembles in the Ising Field Theory
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Integrable quenches in the Hubbard model
• Solution of the BEC to BCS Quench in One Dimension
• Engineering generalized Gibbs ensembles with trapped ions
• Quenches from gaussian bosons to Tonks-Girardeau gas: stationary states and effects of a confining potential
• Superluminal moving defects in the Ising spin chain
• Lack of thermalization for integrability-breaking impurities
• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
• Global Quenches after Localised Perturbations
• Correlation and entanglement spreading in nested spin chains
• Popcorn Drude weights from quantum symmetry
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• The equilibrium landscape of the Heisenberg spin chain
• Hydrodynamic relaxation of spin helices
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Generalized hydrodynamics of integrable quantum circuits
• Spreading of correlations in a quenched repulsive and attractive one dimensional lattice system
• Entanglement Propagation in Integrable Heisenberg Chains from a New Lens
• Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization
• Emergent eigenstate solution for generalized thermalization
• Thermodynamic symmetry resolved entanglement entropies in integrable systems
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles