# Effective response theory for Floquet topological systems

## TL;DR

This paper develops an effective field theory framework using background gauge fields to characterize the topological responses of Floquet systems, including anomalous insulators and group cohomology models, providing new invariants and response functions.

## Contribution

It introduces a novel effective field theory approach for Floquet topological systems using gauge fields within the Schwinger-Keldysh formalism, applicable far from equilibrium.

## Key findings

- Response actions serve as many-body topological invariants.
- Proposes new topological response functions.
- Applicable to chiral Floquet systems and group cohomology models.

## 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 novel topological response functions.