Locality and Heating in Periodically Driven, Power-law Interacting Systems

Periodically driven quantum systems with local interactions take exponentially long to heat up. We study the heating time in periodically driven D-dimensional systems with interaction strengths that decay with the distance r as a power-law 1/r^α. Using a theory based on linear response, we show that the heating time is exponentially long as a function of the drive frequency for α > D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which implies exponentially long heating time for α > 2D. We also generalize recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body 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 bounds from the linear response theory and the Magnus-like expansion does not stem from physical differences in the theories, but rather from 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, and report on recent steps toward achieving this ideal bound for one-dimensional systems.