Multiple localization transitions and novel quantum phases induced by staggered on-site potential

TL;DR

This paper investigates a one-dimensional generalized Aubry-André-Harper model with off-diagonal hopping and staggered on-site potential, revealing multiple reentrant localization transitions and an intermediate phase with coexisting extended, localized, and critical states.

Contribution

It introduces a new generalized AAH model with staggered potential, demonstrating multiple localization transitions and an intermediate phase, expanding understanding of quantum phases in disordered systems.

Findings

Multiple reentrant localization transitions with increasing staggered potential.

Existence of an intermediate phase with coexisting extended, localized, and critical states.

Verification of transitions through quantum static and dynamic measurements.

Abstract

We propose an one-dimensional generalized Aubry-Andr{\'e}-Harper (AAH) model with off-diagonal hopping and staggered on-site potential. We find that the localization transitions could be multiple reentrant with the increasing of staggered on-site potential. The multiple localization transitions are verified by the quantum static and dynamic measurements such as the inversed or normalized participation ratios, fractal dimension and survival probability. Based on the finite-size scaling analysis, we also obtain an interesting intermediate phase where the extended, localized and critical states are coexistent in certain regime of model parameters. These results are quite different from those in the generalized AAH model with off-diagonal hopping, and can help us to find novel quantum phases, new localization phenomena in the disordered systems.