Recent work suggests that a sharp definition of `phase of matter' can be given for some quantum systems out of equilibrium---first for many-body localized systems with time independent Hamiltonians and more recently for periodically driven or Floquet localized systems. In this work we propose a classification of the finite abelian symmetry protected phases of interacting Floquet localized systems in one dimension. We find that the different Floquet phases correspond to elements of $\text{ Cl}\times\mathcal{ A}_G$, where $\text{ Cl}$ is the undriven interacting classification, and $\mathcal{ A}_G$ is a set of (twisted) 1d representations of $G$. We will address symmetry broken phases in a subsequent paper.
Categories: cond-mat.str-el cond-mat.dis-nn