Anomalous mobility edges in one-dimensional quasiperiodic models

TL;DR

This paper introduces and analytically demonstrates the existence of anomalous mobility edges in one-dimensional quasiperiodic models, separating localized states from critical states, with numerical evidence supporting these findings.

Contribution

The study uncovers a new class of mobility edges, termed anomalous, in 1D quasiperiodic models, expanding understanding of localization phenomena beyond traditional cases.

Findings

Analytical proof of anomalous mobility edges in diagonal models

Numerical confirmation of critical state bands via multifractal analysis

Evidence of anomalous mobility edges in off-diagonal Su-Schrieffer-Heeger models

Abstract

Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate bands of localized states from bands of critical states in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite band of critical states. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.