Fate of Many-Body Localization Under Periodic Driving

We study many-body localized quantum systems subject to periodic driving. We find that the presence of a mobility edge anywhere in the spectrum is enough to lead to delocalization for any driving strength and frequency. By contrast, for a fully localized many-body system, a delocalization transition occurs at a finite driving frequency. We present numerical studies on a system of interacting one-dimensional bosons and the quantum random energy model, as well as simple physical pictures accounting for those results.