# Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials

## TL;DR

This paper investigates a one-dimensional quasiperiodic model with off-diagonal and slowly varying diagonal modulations, identifying mobility edges and multiple metal-insulator transitions through theoretical and numerical analysis.

## Contribution

It provides four explicit formulas for mobility edges in a quasiperiodic system with off-diagonal and diagonal modulations, supported by numerical validation.

## Key findings

- Four closed-form expressions for mobility edges.
- Numerical confirmation of theoretical predictions.
- Multiple metal-insulator transitions as energy varies.

## Abstract

We study a one-dimensional system that includes both a commensurate off-diagonal modulation of the hopping amplitude and an incommensurate, slowly varying diagonal on-site modulation. By using asymptotic heuristic arguments, we identify four closed form expressions for the mobility edges. We further study numerically the inverse participation ratio, the density of states and the Lyapunov exponent. The numerical results are in exact agreement with our theoretical predictions. Besides a metal-insulator transition driven by the strength of the slowly varying potential, another four insulator-metal transitions are found in this model as the energy is increased in magnitude from the band center ($E =0$) to the mobility edges ($\pm E_{c2}, \pm E_{c1}$).