



01621nas a2200181   4500008004100000245007900041210006900120260001500189490000800204520106600212100001901278700002001297700002001317700001701337700002301354700002501377856003701402       2019                        eng d00aLocality and Heating in Periodically Driven, Power-law Interacting Systems0 aLocality and Heating in Periodically Driven Powerlaw Interacting  c2019/11/120 v1003 a<p>We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/rα. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α&gt;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 imply exponentially long heating time, for α&gt;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.&nbsp;</p>1 aTran, Minh, C.1 aEhrenberg, Adam1 aGuo, Andrew, Y.1 aTitum, Paraj1 aAbanin, Dmitry, A.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/1908.02773