Scrambling in Ising spin systems with periodic transverse magnetic fields

Abstract: Scrambling of quantum information in both integrable and nonintegrable Floquet spin systems is studied. Our study employs tripartite mutual information (TMI), with negative TMI serving as an indicator of scrambling, where a more negative value suggests a higher degree of scrambling. Both integrable and nonintegrable Floquet systems display scrambling behavior across all periods lying between 0 to {\pi}/2, except at self-dual point({\pi}/4). Nonintegrable Floquet systems exhibit more pronounced scrambling compared to integrable ones across all periods. The degree of scrambling increases as we move towards the self-dual point (but not at the self-dual point), regardless of the initial states. TMI demonstrates periodic behavior at the self-dual point, with a period matching the system size in the case of the integrable system while displaying complex patterns in the non-integrable system. The initial growth of scrambling in both integrable and nonintegrable Floquet systems manifests as a power-law increase for small periods, followed by a sudden jump in scrambling near the self-dual point.