Generalized thermalization in quantum-chaotic quadratic Hamiltonians

TL;DR

This paper demonstrates that in quantum-chaotic quadratic Hamiltonians, certain observables equilibrate in many-body sectors but require the generalized Gibbs ensemble for accurate description, highlighting nuanced thermalization behavior.

Contribution

It proves that eigenstate thermalization in single-particle sectors leads to equilibration in many-body sectors, but not all observables follow eigenstate thermalization, necessitating the generalized Gibbs ensemble.

Findings

Observables with eigenstate thermalization in single-particle sectors equilibrate in many-body sectors.

Many-body sectors contain exponentially many outliers that do not follow eigenstate thermalization.

The generalized Gibbs ensemble accurately describes expectation values after equilibration.

Abstract

Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that exhibit eigenstate thermalization in single-particle sector equilibrate in many-body sectors of quantum-chaotic quadratic models. Remarkably, the same observables do not exhibit eigenstate thermalization in many-body sectors (we establish that there are exponentially many outliers). Hence, the generalized Gibbs ensemble is generally needed to describe their expectation values after equilibration, and it is characterized by Lagrange multipliers that are smooth functions of single-particle energies.