Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
arXiv:1407.8344 · doi:10.1088/1742-5468/2014/10/P10045
Abstract
We consider quantum quenches in the so-called -boson lattice model. We argue that the Generalized Eigenstate Thermalization Hypothesis holds in this model, therefore the Generalized Gibbs Ensemble (GGE) gives a valid description of the stationary states in the long time limit. For a special class of initial states (which are the pure Fock states in the local basis) we are able to provide the GGE predictions for the resulting root densities. We also give predictions for the long-time limit of certain local operators. In the limit the calculations simplify considerably, the wave functions are given by Schur polynomials and the overlaps with the initial states can be written as simple determinants. In two cases we prove rigorously that the GGE prediction for the root density is correct. Moreover, we calculate the exact time dependence of a physical observable (the one-site Emptiness Formation Probability) for the quench starting from the state with exactly one particle per site. In the long-time limit the GGE prediction is recovered.
arXiv comment28 pages, v2: Conclusions extended, references added, and a few minor modifications, v3: minor modifications
References in corpus (43)
- Nonequilibrium dynamics of closed interacting 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 evolution of local observables after quenching to an integrable model
- Dephasing and the steady state in quantum many-particle systems
- Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
- Generalized Thermalization in an Integrable Lattice System
- Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
- Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
- Reduced Density Matrix after a Quantum Quench
- Quantum quench dynamics of the Luttinger model
- Quantum quench dynamics of some exactly solvable models in one dimension
- Solution for an interaction quench in the Lieb-Liniger Bose gas
- Constructing the generalized Gibbs ensemble after a quantum quench
- Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
- On the quantum inverse scattering problem
- Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
- Dynamical Correlations after a Quantum Quench
- 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
- Thermalization and Quantum Correlations in Exactly Solvable Models
- Relaxation of a one-dimensional Mott insulator after an interaction quench
- Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
- Interaction quenches in the 1D Bose gas
- Generalized TBA and generalized Gibbs
- Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
- Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium
- Solution of the quantum inverse problem
- A Gaudin-like determinant for overlaps of Néel and XXZ Bethe states
- Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the 1D Bose gas
- Correlation functions for a strongly correlated boson system
- Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
- Failure of the GGE hypothesis for integrable models with bound states
- An exact formalism for the quench dynamics of integrable models
- Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: Complete relaxation of one-body observables
- Quantum relaxation and finite size effects in the XY chain in a transverse field after global quenches
- Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
- Boxed Plane Partitions as an Exactly Solvable Boson Model
- Short distance correlators in the XXZ spin chain for arbitrary string distributions
- Three-body local correlation function in the Lieb-Liniger model: bosonization approach
- Boxed Skew Plane Partition and Integrable Phase Model
- Equilibration and Generalized GGE in the Lieb Liniger gas
- Quench between a Mott insulator and a Lieb-Liniger liquid
- How to experimentally detect a GGE? - Universal Spectroscopic Signatures of the GGE in the Tonks gas
Cited by in corpus (47)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Generalized Gibbs ensemble in integrable lattice models
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Quantum quenches in 1+1 dimensional conformal field theories
- Entanglement dynamics after quantum quenches in generic integrable systems
- Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
- Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
- Thermalization and light cones in a model with weak integrability breaking
- Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
- Fundamental Asymmetry in Quenches Between Integrable and Nonintegrable Systems
- Quantum quenches in the sine--Gordon model: a semiclassical approach
- Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
- Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
- Pre-relaxation in weakly interacting models
- Memory-preserving equilibration after a quantum quench in a 1d critical model
- Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
- Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
- Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
- Integrability-protected adiabatic reversibility in quantum spin chains
- Exact dynamics following an interaction quench in a one-dimensional anyonic gas
- Approximate light cone effects in a non-relativistic quantum field theory after a local quench
- Non-equilibrium quantum relaxation across a localization-delocalization transition
- Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold
- Test of quantum thermalization in the two-dimensional transverse-field Ising model
- Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
- Quantum relaxation and metastability of lattice bosons with cavity-induced long-range interactions
- Quantum XX-model with competing short- and long-range interactions: Phases and phase transitions in and out of equilibrium
- Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries
- Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
- Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
- Real-Time Evolution in the Hubbard Model with Infinite Repulsion
- Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
- 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
- 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
- Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states
- Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
- An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
- Entanglement prethermalization in the Tomonaga-Luttinger model
- Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
- Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
- Generalized thermalization for integrable system under quantum quench
- Critical quench dynamics of random quantum spin chains: Ultra-slow relaxation from initial order and delayed ordering from initial disorder
- Timescales and necessary conditions for hydrodynamization in one-dimensional Bose gases