Reentrant localization in a quasiperiodic chain with correlated hopping sequences

TL;DR

This paper investigates reentrant localization phenomena in a one-dimensional quasiperiodic system with correlated on-site potentials and structured hopping, revealing how structural correlations influence localization-delocalization transitions.

Contribution

It introduces a model with correlated on-site potentials and structured hopping sequences, demonstrating reentrant localization transitions driven by these correlations.

Findings

Reentrant localization transitions occur due to correlated hopping and potentials.

Structural correlations significantly influence localization behavior.

Parameter regimes for localization and delocalization are identified.

Abstract

Quasiperiodic systems are known to exhibit localization transitions in low dimensions, wherein all electronic states become localized beyond a critical disorder strength. Interestingly, recent studies have uncovered a reentrant localization (RL) phenomenon: upon further increasing the quasiperiodic modulation strength beyond the localization threshold, a subset of previously localized states can become delocalized again within a specific parameter window. While RL transitions have been primarily explored in systems with simple periodic modulations, such as dimerized or long-range hopping integrals, the impact of more intricate or correlated hopping structures on RL behavior remains largely elusive. In this work, we investigate the localization behavior in a one-dimensional lattice featuring staggered, correlated on-site potentials following the Aubry-Andr\'{e}-Harper model, along with off-diagonal hopping modulations structured according to quasiperiodic Fibonacci and Bronze Mean sequences. By systematically analyzing the fractal dimension, inverse participation ratio, and normalized participation ratio, we demonstrate the occurrence of RL transitions induced purely by the interplay between quasiperiodic on-site disorder and correlated hopping. We further examine the parameter space to determine the specific regimes that give rise to RL. Our findings highlight the crucial role of underlying structural correlations in governing localization-delocalization transitions in low-dimensional quasiperiodic systems, where the correlated disorder manifests in both diagonal and off-diagonal terms.