Signature of Chaos and Delocalization in a Periodically Driven Many Body System : An Out-of-Time-Order Correlation Study

TL;DR

This study investigates how out-of-time-order correlations (OTOC) can distinguish localized and delocalized phases in a driven many-body bosonic system, revealing signatures of chaos and delocalization induced by periodic driving.

Contribution

It demonstrates that OTOC can identify drive-induced delocalization in systems lacking a semiclassical limit, using exact numerical methods on driven hardcore bosons with Aubry-André potential.

Findings

OTOC saturation values differentiate localized and delocalized phases

Drive protocols induce distinct physical phenomena

OTOC signatures are experimentally testable

Abstract

We study out-of-time-order correlation (OTOC) for one-dimensional periodically driven hardcore bosons in the presence of Aubry-Andr\'e (AA) potential and show that both the spectral properties and the saturation values of OTOC in the steady state of these driven systems provide a clear distinction between the localized and delocalized phases of these models. Our results, obtained via exact numerical diagonalization of these boson chains, thus indicate that OTOC can provide a signature of drive induced delocalization even for systems which do not have a well defined semiclassical (and/or large N) limit. We demonstrate the presence of such signature by analyzing two different drive protocols for hardcore bosons chains leading to distinct physical phenomena and discuss experiments which can test our theory.