Unveiling quantum criticality of disordered Aubry-Andr\'{e}-Harper models via typical fidelity susceptibility

TL;DR

This paper studies the quantum criticality and localization transition in disordered Aubry-André-Harper models with various potentials, revealing how potential complexity influences localization and critical exponents, with implications for experimental validation.

Contribution

It introduces a detailed analysis of the disordered AAH model with different potentials, highlighting the role of potential complexity and providing critical exponents via fidelity susceptibility.

Findings

Fidelity susceptibility exhibits power-law scaling at the transition.

Critical exponents differ from those in the non-disordered AAH and Anderson models.

Disordered AAH models with different potentials share the same correlation-length exponent.

Abstract

In this study, we investigate the localization transition and quantum criticality {in the ground state of the} disordered Aubry-Andr\'{e}-Harper (AAH) model, where a quasiperiodic potential is hybridized with a disordered potential. In the clean limit, the AAH model undergoes a localization transition from an extended phase to a localized phase via an intermediate critical phase as the strength of the quasiperiodic potential is varied. While the staggered potential merely shifts the critical point to a lower value, Fibonacci and Thue-Morse potentials induce immediate localization. This contrast reveals the sensitivity of localization behavior to the structural complexity of the potential, with the onset of localization correlating with the sequence's complexity. More specifically, the system follows a hierarchy defined by the complexity measures of the applied potentials. In addition, the typical fidelity susceptibility exhibits a power-law scaling behavior at the localization transition, enabling reliable extraction of the critical exponent. We focus on the AAH model with the Fibonacci potential due to its minimal finite-size effects compared to other cases. For the disordered AAH model with the Fibonacci potential, we determine critical exponents that differ from those of the AAH model without disorder and the Anderson model. Moreover, despite differences in localization behavior, we find that the disordered AAH models with the staggered potential and the Fibonacci potential share the same correlation-length critical exponent. These findings provide a unified framework for understanding localization transitions in quasiperiodic systems and are amenable to experimental validation using emerging techniques.