Drive-induced delocalization in the Aubry-André model

Motivated by the recent experiment by Bordia et al. [Nat. Phys. 13, 460 (2017)NPAHAX1745-247310.1038/nphys4020], we study the single particle delocalization phenomena of the Aubry-André (AA) model subjected to periodic drives. In two distinct cases we construct an equivalent classical description to illustrate that the drive-induced delocalization phenomena stems from an instability and the onset of chaos in the underlying dynamics. In the first case we analyze the delocalization and the thermalization in a time modulated AA potential with respect to driving frequency and demonstrate that there exists a threshold value of the amplitude of the drive. In the next example, we show that the periodic modulation of the phase of the hopping amplitude induced by a gauge field leads to an unusual effect on delocalization with a nonmonotonic dependence on the driving frequency. Within a window of such a driving frequency a delocalized Floquet band with a mobility edge appears, exhibiting multifractality in the spectrum as well as in the Floquet eigenfunctions. Finally, we explore the effect of interaction and discuss how the results of the present analysis can be tested experimentally.