Diringer, Asaf A.; Gulden, TobiasISTA
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.
Physical Review B
We thank Y. Bar Lev, T. Biadse, and, particularly, E. Bairey and B. Katzir for illuminating discussions and their many insights and help. The authors thank N. Lindner for his support throughout this project. We are further grateful to M. Serbyn, A. Kamenev, A. Turner, and S. de Nicola for reading the manuscript and providing good feedback and suggestions. We acknowledge financial support from the Defense Advanced Research Projects Agency through the DRINQS program, Grant No. D18AC00025. T.G. was in part supported by an Aly Kaufman Fellowship at the Technion. T.G. acknowledges funding from the Institute of Science and Technology (IST) Austria and from the European Union’s Horizon 2020 research and innovation program under Marie SkłodowskaCurie Grant Agreement No. 754411.under the Marie Skłodowska-Curie Grant Agreement No.754411.
Diringer AA, Gulden T. Impact of drive harmonics on the stability of Floquet many-body localization. Physical Review B. 2021;103(21). doi:10.1103/PhysRevB.103.214204
Diringer, A. A., & Gulden, T. (2021). Impact of drive harmonics on the stability of Floquet many-body localization. Physical Review B. American Physical Society. https://doi.org/10.1103/PhysRevB.103.214204
Diringer, Asaf A., and Tobias Gulden. “Impact of Drive Harmonics on the Stability of Floquet Many-Body Localization.” Physical Review B. American Physical Society, 2021. https://doi.org/10.1103/PhysRevB.103.214204.
A. A. Diringer and T. Gulden, “Impact of drive harmonics on the stability of Floquet many-body localization,” Physical Review B, vol. 103, no. 21. American Physical Society, 2021.
Diringer AA, Gulden T. 2021. Impact of drive harmonics on the stability of Floquet many-body localization. Physical Review B. 103(21), 214204.
Diringer, Asaf A., and Tobias Gulden. “Impact of Drive Harmonics on the Stability of Floquet Many-Body Localization.” Physical Review B, vol. 103, no. 21, 214204, American Physical Society, 2021, doi:10.1103/PhysRevB.103.214204.