Thermalization and Quantum Correlations in Exactly Solvable Models

TL;DR

This paper analytically demonstrates that nonergodic sampling of quantum correlations in exactly solvable models leads to the generalized Gibbs ensemble description after a quantum quench, covering various models and initial states.

Contribution

It establishes an analytical link between nonergodicity of correlations and the validity of the generalized Gibbs ensemble in solvable quantum systems.

Findings

Nonergodicity implies generalized Gibbs ensemble equivalence.

Analytical proof for quantum Ising, XX spin chains, and Luttinger model.

Applicable to local and nonlocal operators and broad initial states.

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.