Exact Floquet flat band and heating suppression via two-rate drive protocols

We demonstrate the existence of exact Floquet flat bands implying strong violation of the eigenstate thermalization hypothesis in a large class of closed quantum many-body systems in the presence of a two-rate drive characterized by frequencies $\Omega_1$ and $\Omega_2=\nu \Omega_1$. We provide the exact analytic condition for this phenomenon to occur for a generic protocol; in particular, $\nu=(2p+1)$, where $p$ is an integer, leads to such flat bands for both square-pulse and cosine drive protocols for arbitrary $\Omega_1$. In the vicinity of these points, heating is suppressed up to very long timescales in such driven systems, leading to a prethermal regime; we demonstrate this by exact numerical studies of distribution and bandwidth of the Floquet eigenstates, spectral form factor, entanglement entropy, and correlation functions of an experimentally realizable finite driven Rydberg chain. The corresponding micromotion exhibits coherent reversal of excitations reminiscent of echoes. Our analysis constitutes a yet unexplored mechanism for heating suppression in driven closed quantum systems.