Robustness of the Floquet many-body localized phase in the presence of a smooth and a non-smooth drive

TL;DR

This study compares how smooth (sine) and non-smooth (square-wave) periodic drives affect the critical amplitude for the Floquet MBL-to-ergodic transition across various frequencies, revealing the role of higher harmonics and resonances.

Contribution

It introduces a numerical method to estimate the frequency dependence of critical driving amplitudes based on drive-induced resonances and compares the effects of different drive smoothness.

Findings

Critical amplitude increases with frequency for both drives.

At high frequencies, both drives have similar critical amplitudes.

Resonances from higher harmonics influence the phase transition behavior.

Abstract

In this work, we investigate how the critical driving amplitude at the Floquet MBL-to-ergodic phase transition differs between smooth and non-smooth driving over a wide range of driving frequencies. To this end, we study numerically a disordered spin-1/2 chain which is periodically driven by a sine or a square-wave drive, respectively. In both cases, the critical driving amplitude increases monotonically with the frequency, and at large frequencies, it is identical for the two drives in the appropriate normalization. However, at low and intermediate frequencies the critical amplitude of the square-wave drive depends strongly on the frequency, while the one of the cosine drive is almost constant in a wide frequency range. By analyzing the density of drive-induced resonance in a Fourier space perspective, 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 to estimate the frequency dependence of the critical driving amplitudes for different drives, based on measuring the density of drive-induced resonances.