Finite-size corrections vs. relaxation after a sudden quench
arXiv:1211.6731 · doi:10.1103/PhysRevB.87.165106
Abstract
We consider the time evolution after sudden quenches of global parameters in translational invariant Hamiltonians and study the time average expectation values and entanglement entropies in finite chains. We show that in noninteracting models the time average of spin correlation functions is asymptotically equal to the infinite time limit in the infinite chain, which is known to be described by a generalized Gibbs ensemble. The equivalence breaks down considering nonlocal operators, and we establish that this can be traced back to the existence of conservation laws common to the Hamiltonian before and after the quench. We develop a method to compute the leading finite-size correction for time average correlation functions and entanglement entropies. We find that large corrections are generally associated to observables with slow relaxation dynamics.
arXiv comment12 pages, 2 figures; V2: minor changes and reference added
References in corpus (64)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- 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
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
- Time-dependence of correlation functions following a quantum quench
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Light-cone-like spreading of correlations in a quantum many-body system
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Quantum Quench in the Transverse Field Ising Chain
- Quantum Quenches in Extended Systems
- Quantum mechanical evolution towards thermal equilibrium
- Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
- Breakdown of thermalization in finite one-dimensional systems
- The Luttinger model following a sudden interaction switch-on
- Interaction Quench in the Hubbard model
- 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
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Generalized Thermalization in an Integrable Lattice System
- Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
- The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Quench dynamics across quantum critical points
- Strongly correlated fermions after a quantum quench
- Quantum quench dynamics of the Luttinger model
- Quantum quench dynamics of some exactly solvable models in one dimension
- Absence of Thermalization in Nonintegrable Systems
- Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
- Effective thermal dynamics following a quantum quench in a spin chain
- Quantum Quenches in Integrable Field Theories
- Localization and Glassy Dynamics Of Many-Body Quantum Systems
- 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
- Dynamical Correlations after a Quantum Quench
- A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
- Entanglement entropy of two disjoint blocks in XY chains
- Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
- Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
- Thermalization and Quantum Correlations in Exactly Solvable Models
- Relaxation of a one-dimensional Mott insulator after an interaction quench
- Quantum quench dynamics of the sine-Gordon model in some solvable limits
- Quantum Quench from a Thermal Initial State
- Time evolution of correlations in strongly interacting fermions after a quantum quench
- Semi-classical theory for quantum quenches in finite transverse Ising chains
- Dynamics in the Ising field theory after a quantum quench
- Quantum relaxation after a quench in systems with boundaries
- Quantum quenches from integrability: the fermionic pairing model
- Fluctuation-dissipation relations and critical quenches in the transverse field Ising chain
- Initial state dependence of the quench dynamics in integrable quantum systems
- Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the 1D Bose gas
- Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model
- Correlations in an expanding gas of hard-core bosons
- Exact infinite-time statistics of the Loschmidt echo for a quantum quench
- On reduced density matrices for disjoint subsystems
- Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories
- Quantum relaxation and finite size effects in the XY chain in a transverse field after global quenches
- Relaxation and Thermalization after a Quantum Quench: Why Localization is Important
- Global large time dynamics and the generalized Gibbs ensemble
- New insights into the entanglement of disjoint blocks
- A new class of completely integrable quantum spin chains
- Semi-classical theory for quantum quenches in the O(3) non-linear sigma model
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- 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
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Reduced Density Matrix after a Quantum Quench
- Solution for an interaction quench in the Lieb-Liniger Bose gas
- Entanglement dynamics after quantum quenches in generic integrable systems
- 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
- Pre-thermalization in a non-integrable quantum spin chain after a quench
- Equilibration of a Tonks-Girardeau gas following a trap release
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
- Interaction quenches in the 1D Bose gas
- Entanglement negativity after a global quantum quench
- Entanglement evolution and generalised hydrodynamics: noninteracting systems
- On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
- Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
- Quench action and Renyi entropies in integrable systems
- Entanglement evolution and generalised hydrodynamics: interacting integrable systems
- Quantum quench from a thermal tensor state: boundary effects and generalized Gibbs ensemble
- Quantum quenches from excited states in the Ising chain
- Equilibration Properties of Classical Integrable Field Theories
- Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
- Pre-relaxation in weakly interacting models
- Rényi entropies after releasing the Néel state in the XXZ spin-chain
- Stationary entanglement entropies following an interaction quench in 1D Bose gas
- Entanglement revivals as a probe of scrambling in finite quantum systems
- Stationary entropies after a quench from excited states in the Ising chain
- Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
- The quench action approach in finite integrable spin chains
- Entanglement and diagonal entropies after a quench with no pair structure
- Non-equilibrium quantum relaxation across a localization-delocalization transition
- Rényi entropies of generic thermodynamic macrostates in integrable systems
- Quantum Quench of the trap frequency in the harmonic Calogero model
- Quantum quenches in two spatial dimensions using chain array matrix product states
- Quench echo and work statistics in integrable quantum field theories
- Prethermalization from a low-density Holstein-Primakoff expansion
- Quantum quenches in the thermodynamic limit. II. Initial ground states
- Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
- Return amplitude after a quantum quench in the XY chain
- Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
- Environment induced pre-thermalization in the Mott-Hubbard model
- Stationary ensemble approximations of dynamic quantum states: Optimizing the Generalized Gibbs Ensemble
- Entanglement prethermalization in the Tomonaga-Luttinger model
- Evolution of the magnetization after a local quench in the critical transverse-field Ising chain
- Critical quench dynamics of random quantum spin chains: Ultra-slow relaxation from initial order and delayed ordering from initial disorder
- Quantum heat waves in a one-dimensional condensate
- Generalized Gibbs ensembles in weakly interacting dissipative systems and digital quantum computers
- Finite time path field theory and a new type of universal quantum spin chain quench behavior
- Finite time path field theory perturbative methods for local quantum spin chain quenches