Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
arXiv:1405.5404 · doi:10.1103/PhysRevA.90.033606
Abstract
Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. Using exact diagonalization and the density matrix renormalization group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. Typically, the relaxation to stationary values occurs over just a few tunneling times. The stationary values are identical to the so-called diagonal ensemble on the system sizes accessible to our numerical methods and we further observe that the micro-canonical ensemble describes the steady state of many observables reasonably well for small and intermediate interaction strength. The expectation values of observables in the canonical ensemble agree quantitatively with the time averages obtained from the quench at small interaction strengths, and qualitatively provide a good description of steady-state values even in parameter regimes where the micro-canonical ensemble is not applicable due to finite-size effects. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis. Moreover, we also observe that the diagonal and the canonical ensemble are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Finally, we discuss implications of our results for the interpretation of a recent sudden expansion experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction quench was realized.
arXiv comment19 pages, 22 figures
References in corpus (107)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- The density-matrix renormalization group in the age of matrix product states
- Cold bosonic atoms in optical lattices
- The density-matrix renormalization group
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- Efficient simulation of one-dimensional quantum many-body 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
- Real time evolution using the density matrix renormalization group
- Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
- Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Relaxation and Pre-thermalization in an Isolated Quantum System
- Light-cone-like spreading of correlations in a quantum many-body system
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Quantum Quenches in Extended Systems
- Quantum mechanical evolution towards thermal equilibrium
- Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
- The approach to thermal equilibrium in quantized chaotic systems
- Breakdown of thermalization in finite one-dimensional systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- The Luttinger model following a sudden interaction switch-on
- Quantum dynamics of a single, mobile spin impurity
- Prethermalization
- Interaction Quench in the Hubbard model
- Exact relaxation in a class of non-equilibrium quantum lattice systems
- Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
- Local emergence of thermal correlations in an isolated quantum many-body system
- Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
- Dephasing and the steady state in quantum many-particle systems
- The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
- Strong and weak thermalization of infinite non-integrable quantum systems
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Alternatives to Eigenstate Thermalization
- Reduced Density Matrix after a Quantum Quench
- Strongly correlated fermions after a quantum quench
- Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions
- Finite-size scaling of eigenstate thermalization
- Constructing the generalized Gibbs ensemble after a quantum quench
- 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
- Quantum quench in an atomic one-dimensional Ising chain
- Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
- Localization and Glassy Dynamics Of Many-Body Quantum Systems
- 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
- Dynamical Correlations after a Quantum Quench
- Eigenstate thermalization within isolated spin-chain systems
- Statistical Theory of Finite Fermi-Systems Based on the Structure of Chaotic Eigenstates
- Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
- Quench Dynamics in a Model with Tuneable Integrability Breaking
- Quantum chaos and thermalization in gapped systems
- Relaxation of a one-dimensional Mott insulator after an interaction quench
- Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids
- Exploring local quantum many-body relaxation by atoms in optical superlattices
- Many-body Landau-Zener dynamics in coupled 1D Bose liquids
- Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
- Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench
- Interaction-induced impeding of decoherence and anomalous diffusion
- Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach
- Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
- Chaos and statistical relaxation in quantum systems of interacting particles
- Emergence of quasi-condensates of hard-core bosons at finite momentum
- Hydrodynamic long-time tails after a quantum quench
- Quench dynamics of the interacting Bose gas in one dimension
- Quantum Chaos in the Bose-Hubbard model
- Recent developments in Quantum Monte-Carlo simulations with applications for cold gases
- Probing local relaxation of cold atoms in optical superlattices
- Initial state dependence of the quench dynamics in integrable quantum systems
- Propagation front of correlations in an interacting Bose gas
- Statistical properties of the spectrum the extended Bose-Hubbard model
- Spin-charge separation in two-component Bose-gases
- Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model
- Luttinger liquid universality in the time evolution after an interaction quench
- Quantum distillation: dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
- Thermalization of Interacting Fermions and Delocalization in Fock space
- Time evolution of one-dimensional Quantum Many Body Systems
- Quench Dynamics of Isolated Many-Body Quantum Systems
- Time Fluctuations in Isolated Quantum Systems of Interacting Particles
- General Features of the Relaxation Dynamics of Interacting Quantum Systems
- Sudden expansion of Mott insulators in one dimension
- Multimode dynamics and emergence of a characteristic length-scale in a one-dimensional quantum system
- Long-time behavior of the momentum distribution during the sudden expansion of a spin-imbalanced Fermi gas in one dimension
- Engineering Local optimality in Quantum Monte Carlo algorithms
- Free expansion of impenetrable bosons on one-dimensional optical lattices
- Locality and thermalization in closed quantum systems
- One-dimensional density waves of ultracold bosons in an optical lattice
- Local versus global equilibration near the bosonic Mott-superfluid transition
- Slow quench dynamics of a trapped one-dimensional Bose gas confined to an optical lattice
- Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models
- Expansion dynamics in the one-dimensional Fermi-Hubbard model
- Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems
- Bogoliubov theory of quantum correlations in the time-dependent Bose-Hubbard model
- Dynamics of correlations in a dilute Bose gas following an interaction quench
- Entangling many-body bound states with propagative modes in Bose-Hubbard systems
- Coherent matter waves emerging from Mott-insulators
- Slow quench dynamics of Mott-insulating regions in a trapped Bose gas
- Spontaneous emissions and thermalization of cold bosons in optical lattices
- Dynamics and evaporation of defects in Mott-insulating clusters of boson pairs
- Eigenvalue statistics of reduced density matrix during driving and relaxation
- Self trapping in the two-dimensional Bose-Hubbard model
- Strong thermalization of the two-component Bose-Hubbard model at finite temperatures
- Comment on "Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined" [arXiv:0810.3720]
- Reply to "Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined' ''
Cited by in corpus (99)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Generalized Gibbs ensemble in integrable lattice models
- Eigenstate Thermalization Hypothesis
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
- Ultracold atoms out of equilibrium
- Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis
- Prethermalization and universal dynamics in near-integrable quantum systems
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Statistical localization: from strong fragmentation to strong edge modes
- Nonthermal states arising from confinement in one and two dimensions
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- Eigenstate thermalization in the two-dimensional transverse field Ising model
- Entanglement and matrix elements of observables in interacting integrable systems
- Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
- Signatures of rare states and thermalization in a theory with confinement
- Many-body localization and thermalization in disordered Hubbard chains
- Eigenstate thermalization and quantum chaos in the Holstein polaron model
- Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
- Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta
- Eigenstate Thermalization, Random Matrix Theory and Behemoths
- Fundamental Asymmetry in Quenches Between Integrable and Nonintegrable Systems
- Many-body localization beyond eigenstates in all dimensions
- Entanglement spreading in non-equilibrium integrable systems
- Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
- Chaos and ergodicity across the energy spectrum of interacting bosons
- Eigenstate thermalization hypothesis and integrals of motion
- One-particle density matrix characterization of many-body localization
- Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
- Slowest local operators in quantum spin chains
- Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model
- Eigenstate thermalization hypothesis through the lens of autocorrelation functions
- Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
- Quantum quenches and many-body localization in the thermodynamic limit
- Eigenstate Thermalization in Systems with Spontaneously Broken Symmetry
- Observation and stabilization of photonic Fock states in a hot radio-frequency resonator
- The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains
- Eigenstate Thermalization Scaling in Majorana Clusters: from Chaotic to Integrable Sachdev-Ye-Kitaev Models
- Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
- Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
- Eigenstate thermalization hypothesis in quantum dimer models
- Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field
- Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
- Nonequilibrium dynamical mean-field theory for bosonic lattice models
- Local entanglement structure across a many-body localization transition
- Coexistence of energy diffusion and local thermalization in nonequilibrium XXZ spin chains with integrability breaking
- Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
- Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"
- Investigating many-body mobility edges in isolated quantum systems
- Non-ergodic behaviour of clean Bose-Hubbard chains
- Quantum quenches in the thermodynamic limit. II. Initial ground states
- Two bosonic quantum walkers in one-dimensional optical lattices
- Interaction quantum quenches in the one-dimensional Fermi-Hubbard model with spin imbalance
- Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach
- Temporal decay of Neel order in the one-dimensional Fermi-Hubbard model
- Numerical linked cluster expansions for quantum quenches in one dimensional lattices
- Chaos in the Bose-Hubbard model and random two-body Hamiltonians
- Reply to "Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"" by Mondaini et.al
- Information-theoretic equilibrium and observable thermalization
- Sudden expansion and domain-wall melting of strongly interacting bosons in two-dimensional optical lattices and on multileg ladders
- Characterizing eigenstate thermalization via measures in the Fock space of operators
- Optimal route to quantum chaos in the Bose-Hubbard model
- Tight-binding billiards
- Spectral analysis of two-dimensional Bose-Hubbard models
- Normal weak eigenstate thermalization
- Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model
- Stable bipolarons in open quantum systems
- Generalized eigenstate typicality in translation-invariant quasifree fermionic models
- Eigenstate Thermalization and Spontaneous Symmetry Breaking in the One-Dimensional Transverse-Field Ising Model with Power-Law Interactions
- Dynamics and level statistics of interacting fermions in the Lowest Landau Level
- Environment induced pre-thermalization in the Mott-Hubbard model
- Eigenstate thermalization scaling in approaching the classical limit
- Entropy and Temperature in finite isolated quantum systems
- Tower of quantum scars in a partially many-body localized system
- Assigning Temperatures to Eigenstates
- Weak ergodicity breaking in Josephson-junction arrays
- Deep reinforcement learning for preparation of thermal and prethermal quantum states
- Properties of the single-site reduced density matrix in the Bose-Bose resonance model in the ground state and in quantum quenches
- Classical route to ergodicity and scarring in collective quantum systems
- Boltzmann relaxation dynamics of strongly interacting spinless fermions on a lattice
- Transient phases and dynamical transitions in the post quench evolution of the generalized Bose-Anderson model
- Diagnosing First and Second Order Phase Transitions with Probes of Quantum Chaos
- Relaxation dynamics of ultracold bosons in a double-well potential: Thermalization and prethermalization in a nearly integrable model
- Back-reaction and correlation effects on pre-thermalization in Mott-Hubbard systems
- Structure of the Hamiltonian of mean force
- Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis
- Interplay of Anderson localization and quench dynamics
- How to seed ergodic dynamics of interacting bosons under conditions of many-body quantum chaos
- Stable interaction-induced Anderson-like localization embedded in standing waves
- Quantum Joule Expansion of One-Dimensional Systems
- Statistical complexity and the road to equilibrium in many-body chaotic quantum systems
- Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system
- Mode folding in systems with local interaction: unitary and non-unitary transformations using tensor states
- Propagation of two-particle correlations across the chaotic phase for interacting bosons
- Chaos and anomalous transport in a semiclassical Bose-Hubbard chain
- Does a Single Eigenstate of a Hamiltonian Encode the Critical Behaviour of its Finite-Temperature Phase Transition?
- Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential
- Basis dependence of eigenstate thermalization