Effective response theory for Floquet topological systems

Abstract

We present an effective field theory approach to the topological response of Floquet systems with symmetry group G. This is achieved by introducing a background G gauge field in the Schwinger-Keldysh formalism, which is suitable for far from equilibrium systems. We carry out this program for chiral topological Floquet systems (anomalous Floquet-Anderson insulators) in two spatial dimensions and the group cohomology models of topological Floquet unitaries. These response actions serve as many-body topological invariants for topological Floquet unitaries. The effective action approach also leads us to propose topological response functions that were not considered before. For a particular family of models, we find that our response theory captures a symmetry protected version of the chiral unitary index.