How periodic driving stabilizes and destabilizes Anderson localization on random trees

Motivated by the link between Anderson localization on high-dimensional graphs and many-body localization, we study the effect of periodic driving on Anderson localization on random trees. The time dependence is eliminated in favor 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 localization problem within the forward scattering approximation (FSA), which we adapt to this extended graph. At low frequency, this favors delocalization as the availability of a large number of extra paths dominates. By contrast, at high frequency, it stabilizes localization compared to the static system. These lead to a regime of re-entrant localization in the phase diagram. Analyzing the statistics of path amplitudes within the FSA, we provide a detailed theoretical picture of the physical mechanisms governing the phase diagram.