Locality and heating in periodically driven, power-law-interacting systems

We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power law $1/r^{\alpha }$ . Using linear-response theory, we show that the heating time is exponentially long as a function of the drive frequency for $\alpha >D$ . For systems that may not obey linear-response theory, we use a more general Magnus-like expansion to show the existence of quasiconserved observables, which imply exponentially long heating time, for $\alpha >2D$ . We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear-response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.