Generalized Thermalization in an Integrable Lattice System

Abstract

After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (~10^10 eigenstates) validate our approach.

8 pages, 9 figures, as published

References in corpus (9)

• Thermalization and its mechanism for generic isolated quantum systems
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• The Luttinger model following a sudden interaction switch-on
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices
• Microscopic expression for the heat in the adiabatic basis

Cited by in corpus (2)

• Finite-size corrections vs. relaxation after a sudden quench
• Initial state dependence of the quench dynamics in integrable quantum systems. III. Chaotic states