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 ${\text{Cl}}_G\times {\mathcal{A}}_G$, where ${\text{Cl}}_G$ is the undriven interacting classification, and ${\mathcal{A}}_G$ is a set of (twisted) one-dimensional representations corresponding to symmetry group $G$. We will address symmetry-broken phases in a subsequent paper C. W. von Keyserlingk and S. L. Sondhi, following paper, Phys. Rev. B 93, 245146 (2016).

• Received 11 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.245145