Localization in One-Dimensional Tight-Binding Model with Chaotic Binary Sequences

TL;DR

This study numerically explores localization phenomena in a one-dimensional tight-binding model with chaotic binary sequences, revealing how correlation parameters influence quantum state localization and transition behaviors.

Contribution

It introduces a detailed analysis of localization properties in a model with chaotic binary on-site energies, highlighting the impact of the stationary-nonstationary transition on quantum localization.

Findings

Lyapunov exponent decay changes from linear to exponential around SNCT

Mean square displacement shows dynamical localization even in nonstationary regimes

Localization length behavior shifts around the SNCT, with deviations from one-parameter scaling for B > 1.5

Abstract

We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition (SNCT). The energy sequences in question might be characterized by their correlation parameter $B$ and the potential strength $W$. The quantum states resulting from such sequences have been characterized in the two ways: Lyapunov exponent at band centre and the dynamics of the initially localized wavepacket. Specifically, the $B-$dependence of the relevant Lyapunov exponent's decay is changing from linear to exponential one around the SNCT ($B \simeq 2$). Moreover, here we show that even in the nonstationary regime, mean square displacement (MSD) of the wavepacket is noticeably suppressed in the long-time limit (dynamical localization). The $B-$dependence of the dynamical localization lengths determined by the MSD exhibits a clear change in the functional behaviour around SNCT, and its rapid increase gets much more moderate one for $B \geq 2$. Moreover we show that the localization dynamics for $B>3/2$ deviates from the one-parameter scaling of the localization in the transient region.