Diringer, Asaf A.; Gulden, TobiasIST Austria
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.
We thank Yevgeny Bar Lev, Eyal Bairey and Barak Katzir for illuminating discussions and their many insights. Especially, the authors thank Netanel Lindner for his support and many comments throughout this project. We are further grateful to Maksym Serbyn 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. TG was in part supported by an Aly Kaufman Fellowship at the Technion. TG acknowledges funding from the Institute of Science and Technology (IST) Austria, and from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No.754411.
Diringer AA, Gulden T. Robustness of the Floquet many-body localized phase in the presence of a smooth and a non-smooth drive. arXiv:200714879.
Diringer, A. A., & Gulden, T. (n.d.). Robustness of the Floquet many-body localized phase in the presence of a smooth and a non-smooth drive. ArXiv:2007.14879. arXiv.
Diringer, Asaf A., and Tobias Gulden. “Robustness of the Floquet Many-Body Localized Phase in the Presence of a Smooth and a Non-Smooth Drive.” ArXiv:2007.14879. arXiv, n.d.
A. A. Diringer and T. Gulden, “Robustness of the Floquet many-body localized phase in the presence of a smooth and a non-smooth drive,” arXiv:2007.14879. arXiv.
Diringer AA, Gulden T. Robustness of the Floquet many-body localized phase in the presence of a smooth and a non-smooth drive. arXiv:2007.14879.
Diringer, Asaf A., and Tobias Gulden. “Robustness of the Floquet Many-Body Localized Phase in the Presence of a Smooth and a Non-Smooth Drive.” ArXiv:2007.14879, 2007.14879, arXiv.