Information Theoretic Signatures of Localization and Mobility Edges in Quasiperiodic Systems

TL;DR

This paper introduces an information theoretic method using Tsallis entropy to distinguish localization transitions and mobility edges in one-dimensional quasiperiodic systems, providing a new diagnostic tool.

Contribution

It develops a novel entropy-gradient susceptibility based on Tsallis entropy that effectively identifies mobility edges and localization transitions in quasiperiodic models.

Findings

The susceptibility peaks sharply at mobility edges, indicating spectral heterogeneity.

The method distinguishes between uniform localization transitions and mobility edge phenomena.

The approach is robust across different entropic parameters q, offering a versatile diagnostic.

Abstract

We investigate localization transitions and mobility edge phenomena in one-dimensional quasiperiodic lattice models using an information theoretic framework based on the Tsallis entropy of single particle eigenstates.We employ the Tsallis entropy as a continuous, normalized functional of wavefunction amplitudes, where the entropic index $q$ provides a tunable sensitivity to different regions of the probability distribution, enhancing the contribution of localized peaks ($q>1$) or extended components ($q<1$). Building on this framework, we introduce an entropy-gradient susceptibility defined from the energy dependence of the Tsallis entropy, which probes variations in eigenstate structure across the spectrum. We show that this quantity clearly distinguishes global localization transitions from mobility edge physics. In the Aubry Andre model, where all eigenstates undergo a uniform transition, the entropy varies smoothly, resulting in a broad crossover in the susceptibility. In contrast, in systems hosting mobility edges, including a quasiperiodically modulated Su Schrieffer Heeger chain and the generalized Aubry Andre model, the coexistence of localized and extended states produces sharp spectral variations, leading to a pronounced and system size independent peak. The qualitative behavior persists over a broad range of the entropic parameter $q$, with systematic variations reflecting its role as a tunable probe of spectral structure. Our results establish an information theoretic approach that leverages the continuous $q$ dependence of Tsallis entropy to construct a derivative based measure of spectral heterogeneity, providing a complementary and physically transparent diagnostic of mobility edge phenomena beyond conventional state resolved measures.