Floquet topological order in interacting systems of bosons and fermions

Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We show that these drives have surprising many-body analogs, applicable to generic systems of bosons, fermions or spins, which demonstrate anomalous transport of charge or information at the edge. We characterize systems of this kind by studying their edge behavior, defining a notion of dynamical topological order that may be applied to general time-dependent systems, including many-body localized phases or time crystals. We go on to discuss symmetry-protected generalizations of these drives.