# Interacting invariants for Floquet phases of fermions in two dimensions

## TL;DR

This paper introduces a new invariant for two-dimensional Floquet phases of interacting fermions, enabling distinction between trivial and non-trivial phases, including those with topological order and edge chiral pumping.

## Contribution

It generalizes Floquet invariants to interacting fermions, capturing topological and symmetry properties, and links bulk anyonic symmetry to edge chirality.

## Key findings

- Invariant distinguishes trivial and anomalous Floquet phases.
- Invariant detects Kitaev chain pumping in fermionic models.
- Nonzero invariant indicates exchange of electric and magnetic excitations.

## Abstract

We construct a many-body quantized invariant that sharply distinguishes among two dimensional non-equilibrium driven phases of interacting fermions. This is an interacting generalization of a band-structure Floquet quasi-energy winding number, and describes chiral pumping of quantum information along the edge. In particular, our invariant sharply distinguishes between a trivial and anomalous Floquet Anderson insulator in the interacting, many-body localized setting. It also applies more generally to models where only fermion parity is conserved, where it differentiates between trivial models and ones that pump Kitaev Majorana chains to the boundary, such as ones recently introduced in the context of emergent fermions arising from eigenstate $\Z_2$ topological order. We evaluate our invariant for the edge of such a system with eigenstate $\Z_2$ topological order, and show that it is necessarily nonzero when the Floquet unitary exchanges electric and magnetic excitations, proving a connection between bulk anyonic symmetry and edge chirality.