Drive-induced delocalization in the Aubry-André model

Abstract

Motivated by the recent experiment by Bordia et al [Nat. Phys. 13, 460 (2017)], we study single particle delocalization phenomena of 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 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 hopping amplitude leads to an unusual effect on delocalization with a non-monotonic dependence on the driving frequency. Within a window of such driving frequency a delocalized Floquet band with 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. PACS numbers:Introduction: Periodically driven quantum systems have been extensively used to study various phenomena like parametric resonance, quantum chaos, topological phases, etc [1][2][3][4][5]. Experimental and theoretical studies have gained interests in the context of many body systems exhibiting thermalization in the presence of a periodic drive [6][7][8][9][10]. On the other hand the fate of a driven many body localized (MBL) state is an emerging issue [11,12] as has been demonstrated in a seminal experiment on ultra-cold atomic systems showing delocalization from the MBL phase [7]. It is a pertinent question to ask how generic is this phenomenon and whether there is any underlying principle that explains drive induced delocalization of MBL phase.

Localisation transition in the driven Aubry-André model

“…For these plots we considered a frequency ν = ω/2π = 0.005(1/J). The same value for the critical amplitude was found in [23].…”

“…the periodically driven Aubry-André model, in order to understand which kind of effects can be disentangled from a strict many-body description. The same model was recently studied in [23], with which our results show good agreement, particularly in estimating the critical amplitude.…”

Interaction-induced long-time tail of a nonlinear ac absorption in a localized system: A relay-race mechanism

“…To estimate the effect of feedback, we take the expression for S a z (t)S b z (t) obtained in the lowest order and substitute it into (10). The expression for S a z (t)S b z (t) has the form similar to the expression for S a z (t)S a z (t ) in (12)…”

Spinful Aubry-André model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling

“…[3][4][5] Early studies of the AA model [6][7][8][9][10][11] were focused on the properties of localized eigenfunctions near the transition. Lately, the interest to the AA model has been revived [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] . Nowadays, it is invoked to study different observable quantities in the presence of the quasiperiodic background.…”

“…Experimental advances motivated new theoretical studies towards the extension of the AA model. These studies include incorporation of interaction effects 15,16 , effects of the ac-drive 22 , and the dynamics of a quench 18,24 .…”