Thermalization in Systems with Bipartite Eigenmode Entanglement

Abstract

It is analytically shown that the asymptotic correlations in exactly solvable models following a quantum quench can behave essentially as thermal correlations provided the entanglement between two eigenmodes is sufficiently strong. We provide one example and one counter example of this observation. The example illustrates the fact that the thermal correlations arise from initial states where the entanglement between the eigenmodes stems from the existence of a large energy gap in the initial state. On the other hand, the counter-example shows that when the bi-partite entanglement of the eigenmodes stems from interactions that do not open a gap, the correlations at asymptotically long times are non-thermal. We also show that the thermal behavior concerns only the asymptotic correlation functions, as the difference with an actual thermal ensemble can be observed measuring the energy fluctuations of the system. The latter observation implies a breakdown of the fluctuation-dissipation theorem.

8 pages

References in corpus (29)

• Thermalization and its mechanism for generic isolated quantum systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Foundation of Statistical Mechanics under experimentally realistic conditions
• The Luttinger model following a sudden interaction switch-on
• Interaction Quench in the Hubbard model
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Dephasing and the steady state in quantum many-particle systems
• Quench dynamics across quantum critical points
• Strongly correlated fermions after a quantum quench
• Quantum quench dynamics of the Luttinger model
• Defect production in non-linear quench across a quantum critical point
• 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
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Entropy of isolated quantum systems after a quench
• Thermalization and Quantum Correlations in Exactly Solvable Models
• The dynamics and prethermalization of one dimensional quantum systems probed through the full distributions of quantum noise
• Quantum quench dynamics of the sine-Gordon model in some solvable limits
• Quantum Quench from a Thermal Initial State
• Mode coupling induced dissipative and thermal effects at long times after a quantum quench
• Quantum quenches from integrability: the fermionic pairing model
• Initial state dependence of the quench dynamics in integrable quantum systems
• Intrinsic dephasing in one dimensional ultracold atom interferometers
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• On the relation between entanglement and subsystem Hamiltonians
• Thermalization in a one-dimensional integrable system

Cited by in corpus (17)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Ballistic front dynamics after joining two semi-infinite quantum Ising chains
• Fate of Majorana fermions and Chern numbers after a quantum quench
• Measuring effective temperatures in a generalized Gibbs ensemble
• Initial state dependence of the quench dynamics in integrable quantum systems. III. Chaotic states
• Edge mode dynamics of quenched topological wires
• Equilibration and GGE for hard wall boundary conditions
• Momentum-space entanglement and Loschmidt echo in Luttinger liquids after a quantum quench
• Splitting a critical spin chain
• Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Relaxation of the entanglement spectrum in quench dynamics of topological systems
• Effective temperature from fluctuation-dissipation theorem in systems with bipartite eigenmode entanglement
• Exact results, transient generalized Gibbs ensembles, and analytic approximations for spacetime propagators of massive, real scalar fields in one spatial dimension