Prethermalisation and Thermalisation in the Entanglement Dynamics

Abstract

We investigate the crossover of the entanglement entropy towards its thermal value in nearly integrable systems. We employ equation of motion techniques to study the entanglement dynamics in a lattice model of weakly interacting spinless fermions after a quantum quench. For weak enough interactions we observe a two-step relaxation of the entanglement entropies of finite subsystems. Initially the entropies follow a nearly integrable evolution, approaching the value predicted by the Generalized Gibbs Ensemble (GGE) of the unperturbed model. Then, they start a slow drift towards the thermal stationary value described by a standard Gibbs Ensemble (GE). While the initial relaxation to the GGE is independent of the interaction, the slow drift from GGE to GE values happens on time scales proportional to the inverse interaction squared. For asymptotically large times and subsystem sizes the dynamics of the entropies can be predicted using a modified quasiparticle picture that keeps track of the evolution of the fermionic occupations caused by the integrability breaking. This picture gives a quantitative description of the results as long as the integrability-breaking timescale is much larger than the one associated with the (quasi) saturation to the GGE. In the opposite limit the quasiparticle picture still provides the correct late-time behaviour, but it underestimates the initial slope of the entanglement entropy.

15 pages, 8 figures; v2 as appears in Phys. Rev. B

References in corpus (33)

• Many-Body Physics with Ultracold Gases
• Many body localization and thermalization in quantum statistical mechanics
• Black holes as mirrors: quantum information in random subsystems
• Many body localization in Heisenberg XXZ magnet in a random field
• Experimental Observation of a Generalized Gibbs Ensemble
• Interaction Quench in the Hubbard model
• Entropy scaling and simulability by Matrix Product States
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Quench dynamics across quantum critical points
• Holographic Evolution of Entanglement Entropy
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Metastable superfluidity of repulsive fermionic atoms in optical lattices
• On entropy growth and the hardness of simulating time evolution
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Thermalization and light cones in a model with weak integrability breaking
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Entanglement dynamics in short and long-range harmonic oscillators
• Exploring dynamical phase transitions and prethermalization with quantum noise of excitations
• Entanglement in a periodic quench
• On the theory of quantum quenches in near-critical systems
• Pre-relaxation in weakly interacting models
• Exact solution for the quench dynamics of a nested integrable system
• Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids
• Entanglement growth and simulation efficiency in one-dimensional quantum lattice systems
• Quantum quenches with integrable pre-quench dynamics
• Global large time dynamics and the generalized Gibbs ensemble
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Matrix-valued Boltzmann Equation for the Hubbard Chain
• Thermalization rates in the one dimensional Hubbard model with next-to-nearest neighbor hopping
• Glass-like Behavior in a System of One Dimensional Fermions after a Quantum Quench
• Equations of Motion for the Out-of-Equilibrium Dynamics of Isolated Quantum Systems from the Projection Operator Technique