Classification of Interacting Floquet Phases with U(1) Symmetry

Recently, it has become clear that periodically driven many-body systems can support new types of topological phases that have no counterpart in static systems. These anomalous Floquet topological phases have been studied for both interacting and non-interacting systems in different symmetry classes. In this talk, we consider interacting Floquet topological phases with U(1) charge conservation symmetry in two spatial dimensions. We propose a complete classification of Floquet phases of this kind, in the case where the Floquet eigenstates are short-range entangled, and we show that each phase can be labeled by a topological invariant which can be computed either at the edge of an open system or in the bulk. The latter formula provides a way to measure the invariant and also reveals a connection to the bulk magnetization density discussed in previous work.