Single-particle and many-body analyses of a quasiperiodic integrable system after a quench

TL;DR

This paper investigates how localization in a quasiperiodic system affects the relaxation dynamics of noninteracting particles, revealing distinct behaviors at localization transitions and supporting a Gaussian equilibration framework.

Contribution

It provides a combined single-particle and many-body analysis of localization effects on relaxation in the Aubry-Andre model, highlighting the role of localization in nonthermalization.

Findings

Relaxation behaviors differ between localized, delocalized, and critical regimes.

Some observables do not relax in certain regimes, while others do, consistent with Gaussian equilibration.

Localization influences the properties of statistical ensembles derived from many-body eigenstates.

Abstract

In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-Andre model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics of the momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character. We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties.