Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics

TL;DR

This paper explores how periodic and aperiodic drives affect long-range quantum systems, revealing drive-induced phases, dynamical localization, and contrasting behaviors in different models through spectral and transport analysis.

Contribution

It introduces a comprehensive analysis of driven long-range systems, uncovering drive-induced fractal phases, exact dynamical localization, and differences between periodic, aperiodic, and quasi-periodic driving.

Findings

Drive-induced fractal phase with diffusive transport

Exact dynamical localization at special drive parameters

Diffusive and subdiffusive transport behaviors in different regimes

Abstract

We investigate the electric-field driven power-law random banded matrix(PLRBM) model where a variation in the power-law exponent $\alpha$ yields a delocalization-to-localization phase transition. We examine the periodically driven PLRBM model with the help of the Floquet operator. The level spacing ratio and the generalized participation ratio of the Floquet Hamiltonian reveal a drive-induced fractal phase accompanied by diffusive transport on the delocalized side of the undriven PLRBM model. On the localized side, the time-periodic model remains localized - the average spacing ratio corresponds to Poisson statistics and logarithmic transport is observed in the dynamics. Extending our analysis to the aperiodic Thue-Morse (TM) driven system, we find that the aperiodically driven clean long-range hopping model (clean counterpart of the PLRBM model) exhibits the phenomenon of \textit{exact dynamical localization} (EDL) on tuning the drive-parameters at special points. The disordered time-aperiodic system shows diffusive transport followed by relaxation to the infinite-temperature state on the delocalized side, and a prethermal plateau with subdiffusion on the localized side. Additionally, we compare this with a quasi-periodically driven AAH model that also undergoes a localization-delocalization transition. Unlike the disordered long-range model, it features a prolonged prethermal plateau followed by subdiffusion to the infinite temperature state, even on the delocalized side.