Characterization of Thermalization Behaviour in a Generalized Aubry-Andr\'e Model

TL;DR

This paper investigates the ergodic to many-body localized transition in a generalized Aubry-Andre9 model with interactions, using spectral analysis and finite-size scaling to characterize critical behavior.

Contribution

It introduces a phase diagram based on the Frobenius norm of an adiabatic gauge potential and analyzes spectral statistics to understand the transition.

Findings

Identifies the critical disordered strength for the transition.

Shows the scaling behavior of the Thouless time with disorder.

Provides a finite-size scaling analysis of the transition point.

Abstract

Although random matrix theory provides a fundamental framework for characterizing quantum chaos, encompassing both ergodic and localized phases, a comprehensive understanding of the universal features governing the critical transition remains elusive in many disordered and quasi-random systems. In this study, we explore the ergodic-to-many-body localization transition in the generalized Aubry-Andr\'e model with interacting spinless fermions. Using the concept of Frobenius norm of an adiabatic gauge potential, we construct a phase diagram that captures the sensitivity of the eigenspectrum to infinitesimal adiabatic gauge deformations. To examine the stability of the critical disordered strength with respect to system size, we perform an unbiased finite-size scaling analysis via cost-function minimization techniques. Additionally, by analyzing the adjacent gap ratio and spectral form factor, we determine the scaling behavior of the Thouless time as a function of the disorder strength.