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We propose a mechanism to suppress heating in periodically driven many-bodyquantum systems by employing sufficiently long-range interactions andexperimentally relevant initial conditions. The mechanism is robust to localperturbations and does \emph{not} rely on disorder or high driving frequencies.Instead, it makes use of an approximate fragmentation of the many-body spectrumof the non-driven system into bands, with band gaps that grow with the systemsize. We show that when these systems are driven, there is a regime where\emph{decreasing} the driving frequency \emph{decreases} heating andentanglement build-up. This is demonstrated numerically for a prototypicalsystem of spins in one dimension, but the results can be readily generalized tohigher dimensions.

Suppression of heating by long-range interactions in periodically driven spin chains