Thermalization and Quantum Correlations in Exactly Solvable Models

Abstract

The generalized Gibbs ensemble introduced for describing few body correlations in exactly solvable systems following a quantum quench is related to the nonergodic way in which operators sample, in the limit of infinite time after the quench, the quantum correlations present in the initial state. The nonergodicity of the correlations is thus shown \emph{analytically} to imply the equivalence with the generalized Gibbs ensemble for quantum Ising and XX spin chains as well as for the Luttinger model the thermodynamic limit, and for a broad class of initial states and correlation functions of both local and nonlocal operators.

12 pages, 4 figures. Expanded in response to Referee criticism

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Cited by in corpus (119)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
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• Generalized Gibbs ensemble in integrable lattice models
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• Time evolution of local observables after quenching to an integrable model
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• Quantum quenches in 1+1 dimensional conformal field theories
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• Alternatives to Eigenstate Thermalization
• Reduced Density Matrix after a Quantum Quench
• Entanglement dynamics after quantum quenches in generic integrable systems
• Periodic thermodynamics of isolated systems
• Prethermalization and universal dynamics in near-integrable quantum systems
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
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• Dynamical Correlations after a Quantum Quench
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Validity of the GGE for quantum quenches from interacting to noninteracting models
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• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Quantum quench in the sine-Gordon model
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Interaction quenches in the 1D Bose gas
• Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench
• On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
• Dynamics in the Ising field theory after a quantum quench
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
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• Entanglement and quantum transport in integrable systems
• Quench action and Renyi entropies in integrable systems
• Generalized Gibbs Ensemble for Heisenberg Spin Chains
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
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• Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
• Quantum Quench and Prethermalization Dynamics in A Two-Dimensional Fermi Gas with Long-range Interactions
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• Memory-preserving equilibration after a quantum quench in a 1d critical model
• Exact solution for the quench dynamics of a nested integrable system
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• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Single-particle and many-body analyses of a quasiperiodic integrable system after a quench
• Entanglement revivals as a probe of scrambling in finite quantum systems
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• Relaxation and Thermalization after a Quantum Quench: Why Localization is Important
• Relaxation Dynamics of Disordered Spin Chains: Localization and the Existence of a Stationary State
• Thermalization under randomized local Hamiltonians
• Interaction quench in a trapped one-dimensional Bose gas
• Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains
• Quantum quench in long-range field theories
• The quench action approach in finite integrable spin chains
• Non-equilibrium quantum relaxation across a localization-delocalization transition
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• Efimov Physics in Quenched Unitary Bose Gases
• Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
• Relaxation to gaussian and generalized Gibbs states in systems of particles with quadratic hamiltonians
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• Relaxation dynamics of two coherently coupled one-dimensional bosonic gases
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• Nonequilibrium quench dynamics in quantum quasicrystals
• Universal Features of the Excitation Spectrum in Generalized Gibbs Distribution Ensemble
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• Dynamical depinning of a Tonks Girardeau gas
• Quench Dynamics of Topological Maximally-Entangled States
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• Entanglement Dynamics between Ising Spins and a Central Ancilla
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
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• Theoretical study on thermalization in isolated quantum systems