Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials

TL;DR

This paper introduces a universal analytical ansatz for the mobility edge in various one-dimensional quasiperiodic models, validated by numerical calculations, aiding in predicting localized and extended states in complex systems.

Contribution

The authors propose a single simple ansatz that accurately predicts mobility edges across diverse quasiperiodic models, including nonsinusoidal potentials and long-range hopping.

Findings

The ansatz matches known limits of the Aubry-André model.

It applies to many nonsinusoidal and long-range models.

It provides a practical tool for estimating mobility edges.

Abstract

We obtain approximate solutions defining the mobility edge separating localized and extended states for several classes of generic one-dimensional quasiperiodic models. We validate our analytical ansatz with exact numerical calculations. Rather amazingly, we provide a single simple ansatz for the generic mobility edge, which is satisfied by quasiperiodic models involving many different types of nonsinusoidal incommensurate potentials as well as many different types of long-range hopping models. Our ansatz agrees precisely with the well-known limiting cases of the sinusoidal Aubry-Andr\'{e} model (which has no mobility edge) and the generalized Aubry-Andr\'{e} models (which have analytical mobility edges). Our work provides a practical tool for estimating the location of mobility edges in quasiperiodic systems.