Localization and transport in a strongly driven Anderson insulator

We study localization and charge dynamics in a monochromatically driven one-dimensional Anderson insulator focussing on the low-frequency, strong-driving regime. We study this problem using a mapping of the Floquet Hamiltonian to a hopping problem with correlated disorder in one higher harmonic-space dimension. We show that (i) resonances in this model correspond to \emph{adiabatic} Landau-Zener (LZ) transitions that occur due to level crossings between lattice sites over the course of dynamics; (ii) the proliferation of these resonances leads to dynamics that \emph{appear} diffusive over a single drive cycle, but the system always remains localized; (iii) actual charge transport occurs over many drive cycles due to slow dephasing between these LZ orbits and is logarithmic-in-time, with a crucial role being played by far-off Mott-like resonances; and (iv) applying a spatially-varying random phase to the drive tends to decrease localization, suggestive of weak-localization physics. We derive the conditions for the strong driving regime, determining the parametric dependencies of the size of Floquet eigenstates, and time-scales associated with the dynamics, and corroborate the findings using both numerical scaling collapses and analytical arguments.