We investigate how the critical driving amplitude at the Floquet many-body localized (MBL) to ergodic phase transition differs between smooth and nonsmooth drives. To this end, we numerically study a disordered spin-1/2 chain which is periodically driven by a sine or square-wave drive over a wide range of driving frequencies. In both cases the critical driving amplitude increases monotonically with the frequency, and at large frequencies it is identical for the two drives. However, at low and intermediate frequencies the critical amplitude of the square-wave drive depends strongly on the frequency, while that of the sinusoidal drive is almost constant over a wide frequency range. By analyzing the density of drive-induced resonances we conclude that this difference is due to resonances induced by the higher harmonics which are present (absent) in the Fourier spectrum of the square-wave (sine) drive. Furthermore, we suggest a numerically efficient method for estimating the frequency dependence of the critical driving amplitudes for different drives which is based on calculating the density of drive-induced resonances. We conclude that delocalization occurs once the density of drive-induced resonances reaches a critical value determined only by the static system.

中文翻译：

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驱动谐波对 Floquet 多体定位稳定性的影响

我们研究了 Floquet 多体局部化 (MBL) 到遍历相变的临界驱动振幅在平滑和非平滑驱动之间有何不同。为此，我们对无序自旋 1/2 链进行了数值研究，该链由正弦波或方波驱动器在很宽的驱动频率范围内周期性地驱动。在这两种情况下，临界驱动幅度随频率单调增加，并且在大频率下，这两种驱动是相同的。然而，在低频和中频，方波驱动的临界幅度很大程度上取决于频率，而正弦驱动的临界幅度在很宽的频率范围内几乎是恒定的。通过分析驱动引起的共振密度，我们得出结论，这种差异是由于方波（正弦）驱动的傅立叶频谱中存在（不存在）的高次谐波引起的共振造成的。此外，我们提出了一种数值有效的方法，用于估计不同驱动器的临界驱动振幅的频率依赖性，该方法基于计算驱动引起的共振密度。我们得出结论，一旦驱动引起的共振密度达到仅由静态系统确定的临界值，就会发生离域。我们建议采用一种数值有效的方法来估计不同驱动器的临界驱动振幅的频率依赖性，该方法基于计算驱动引起的共振密度。我们得出结论，一旦驱动引起的共振密度达到仅由静态系统确定的临界值，就会发生离域。我们提出了一种数值有效的方法来估计不同驱动器的临界驱动振幅的频率依赖性，该方法基于计算驱动引起的共振密度。我们得出结论，一旦驱动引起的共振密度达到仅由静态系统确定的临界值，就会发生离域。