Dynamical Freezing and Scar Points in Strongly Driven Floquet Matter: Resonance vs Emergent Conservation Laws

We consider a clean quantum system subject to strong periodic driving. The existence of a dominant energy scale, $h_D^x$, can generate considerable structure in an effective description of a system which, in the absence of the drive, is non-integrable, interacting, and does not host localization. In particular, we uncover points of freezing in the space of drive parameters (frequency and amplitude). At those points, the dynamics is severely constrained due to the emergence of an almost exact local conserved quantity, which scars the {it entire} Floquet spectrum by preventing the system from heating up ergodically, starting from any generic state, even though it delocalizes over an appropriate subspace. At large drive frequencies, where a naive Magnus expansion would predict a vanishing effective (average) drive, we devise instead a strong-drive Magnus expansion in a moving frame. There, the emergent conservation law is reflected in the appearance of an `integrability of an effective Hamiltonian. These results hold for a wide variety of Hamiltonians, including the Ising model in a transverse field in {it any dimension} and for {it any form of Ising interactions}. The phenomenon is also shown to be robust in the presence of {it two-body Heisenberg interactions with any arbitrary choice of couplings}. Further, we construct a real-time perturbation theory which captures resonance phenomena where the conservation breaks down, giving way to unbounded heating. This opens a window on the low-frequency regime where the Magnus expansion fails.