Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs

TL;DR

This paper investigates how the Thouless time scales with system size in the Anderson model on random regular graphs, revealing a sub-diffusive regime that precedes localization, using spectral analysis and Floquet modifications.

Contribution

It demonstrates the sub-diffusive scaling of the Thouless time in the Anderson model on random regular graphs, including a Floquet version to mitigate finite-size effects.

Findings

Thouless time exhibits sub-diffusive scaling before localization.

Spectral form factor and power spectrum effectively determine Thouless time.

Floquet model confirms sub-diffusive regime independent of energy conservation.

Abstract

The scaling of the Thouless time with system size is of fundamental importance to characterize dynamical properties in quantum systems. In this work, we study the scaling of the Thouless time in the Anderson model on random regular graphs with on-site disorder. We determine the Thouless time from two main quantities: the spectral form factor and the power spectrum. Both quantities probe the long-range spectral correlations in the system and allow us to determine the Thouless time as the time scale after which the system is well described by random matrix theory. We find that the scaling of the Thouless time is consistent with the existence of a sub-diffusive regime anticipating the localized phase. Furthermore, to reduce finite-size effects, we break energy conservation by introducing a Floquet version of the model and show that it hosts a similar sub-diffusive regime.