  We explore how disorder and interactions conspire in lattice models with
sequentially activated hopping to produce novel k-body (or many-body) localized
phases. Specifically, we show that when disorder is added to the set of
interacting floquet models considered in [Wampler and Klich arXiv:2209.09180],
regions in parameter space near the special points where classical-like
dynamics emerge are stabilized prethermally (or via many-body localization in
some cases) producing new families of interesting phases. We also find that
this disordered system exhibits novel phases in regions of parameter space away
from the special, Diophantine points. Furthermore, the regions in parameter
space where Hilbert space fragmentation occurs in the clean system (leading to
Krylov subspaces exhibiting frozen dynamics, cellular automation, and subspaces
exhibiting signs of ergodic behavior) may also be stabilized by the addition of
disorder. This leads to the emergence of exotic dynamics within the Krylov
subspace.
