Generalized thermalization for integrable system under quantum quench

Abstract

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the Generalized Gibbs Ensemble description for this infinite dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve towards the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a Generalized Gibbs Ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states which would potentially not be described by the Gibbs Generalized Ensemble description.

15 pages, 9 figures; To appear in Phys. Rev. E

References in corpus (25)

• Thermalization and its mechanism for generic isolated quantum systems
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Generalized Gibbs ensemble in integrable lattice models
• Experimental Observation of a Generalized Gibbs Ensemble
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Generalized Thermalization in an Integrable Lattice System
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Ultracold atoms out of equilibrium
• Quantum quench dynamics of the Luttinger model
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Evolution of entanglement after a local quench
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
• Entanglement evolution after connecting finite to infinite quantum chains
• Stationary states in a free fermionic chain from the Quench Action Method
• Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• Lower Bounding Diffusion Constant by the Curvature of Drude Weight
• Entanglement and discord: accelerated observations of local and global modes
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction
• Real-time dynamics in a strongly interacting bosonic hopping model: Global quenches and mapping to the XX chain

Cited by in corpus (5)

• Dynamical Fermionization in One Dimensional Spinor Gases
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
• Out of Time Order Correlations in the Quasi-Periodic Aubry-André model
• Steady-states of out-of-equlibrium inhomogeneous Richardson-Gaudin quantum integrable models in quantum optics
• Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges