How periodic driving stabilises and destabilises Anderson localisation on random trees

TL;DR

This paper investigates how periodic driving influences Anderson localisation on random trees, revealing that low frequencies promote delocalisation while high frequencies stabilize localisation, leading to re-entrant phase transitions.

Contribution

It introduces a novel approach by mapping periodic driving to an extended graph and adapts the forward scattering approximation to analyze localisation effects.

Findings

Low frequency drives promote delocalisation.

High frequency drives stabilize localisation.

Re-entrant localisation phase observed.

Abstract

Motivated by the link between Anderson localisation on high-dimensional graphs and many-body localisation, we study the effect of periodic driving on Anderson localisation on random trees. The time dependence is eliminated in favour of an extra dimension, resulting in an extended graph wherein the disorder is correlated along the new dimension. The extra dimension increases the number of paths between any two sites and allows for interference between their amplitudes. We study the localisation problem within the forward scattering approximation (FSA) which we adapt to this extended graph. At low frequency, this favours delocalisation as the availability of a large number of extra paths dominates. By contrast, at high frequency, it stabilises localisation compared to the static system. These lead to a regime of re-entrant localisation in the phase diagram. Analysing the statistics of path amplitudes within the FSA, we provide a detailed theoretical picture of the physical mechanisms governing the phase diagram.