Estimating critical disorder strength of an AAH system via thermal response

TL;DR

This paper introduces a novel thermal response method, using specific heat measurements, to accurately identify the critical disorder strength in the Aubry-Andre9-Harper model, offering a new experimental probe for localization transitions.

Contribution

The study proposes using electronic specific heat as a sensitive indicator of the localization transition in the AAH model, providing a new thermal-based approach to detect critical disorder strength.

Findings

Specific heat exhibits a distinctive signature at the transition

Numerical analysis confirms thermal response as an effective probe

Method facilitates experimental detection of localization transition

Abstract

The Aubry-Andr\'e-Harper (AAH) model provides a paradigmatic platform to study localization phenomena, where a transition from a conducting to an insulating phase occurs at a critical disorder strength equal to twice the nearest-neighbor hopping amplitude, $2t$. While this transition has been explored extensively through various probes, here we propose a fundamentally new approach based on thermal response. Specifically, we demonstrate that the electronic specific heat exhibits a distinctive signature across the transition, directly reflecting the anomalous evolution of the density of states with disorder strength. Our findings, supported by numerical analysis, establish specific heat measurement as a powerful and sensitive probe for detecting the critical point. This thermal characterization opens a new avenue for exploring disorder-induced phase transitions and paves the way for experimental realization in engineered quantum systems.