Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems

TL;DR

This paper demonstrates that prethermalization plateaus in nearly integrable quantum systems can be accurately predicted by generalized Gibbs ensembles, linking their relaxation behavior to nonthermal steady states in integrable systems.

Contribution

It shows that generalized Gibbs ensembles can predict prethermalization plateaus, connecting the dynamics of integrable and nearly integrable quantum systems.

Findings

Prethermalization plateaus are correctly predicted by generalized Gibbs ensembles.

Nonthermal steady states in integrable systems are akin to prethermalized states that do not decay.

Relaxation behaviors of integrable and nearly integrable systems are described by the same statistical theory.

Abstract

A quantum many-body system which is prepared in the ground state of an integrable Hamiltonian does not directly thermalize after a sudden small parameter quench away from integrability. Rather, it will be trapped in a prethermalized state and can thermalize only at a later stage. We discuss several examples for which this prethermalized state shares some properties with the nonthermal steady state that emerges in the corresponding integrable system. These examples support the notion that nonthermal steady states in integrable systems may be viewed as prethermalized states that never decay further. Furthermore we show that prethermalization plateaus are under certain conditions correctly predicted by generalized Gibbs ensembles, which are the appropriate extension of standard statistical mechanics in the presence of many constants of motion. This establishes that the relaxation behaviors of integrable and nearly integrable systems are continuously connected and described by the same statistical theory.