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

Fragmentation and Novel Prethermal Dynamical Phases in Disordered, Strongly-Interacting Floquet Systems