Bulk-boundary correspondence for interacting Floquet systems in two dimensions

TL;DR

This paper introduces a new method to derive bulk and edge invariants for interacting Floquet systems in two dimensions, advancing understanding of topological phases in many-body localized systems.

Contribution

It develops a mathematical framework based on a flow object to compute invariants for interacting Floquet systems, including those with symmetries, and reformulates known invariants.

Findings

Derived bulk invariants for symmetry and no-symmetry systems

Established a bulk counterpart to the GNVW index for bosonic systems

Provided new formulations of existing single-particle and many-body invariants

Abstract

We present a method for deriving bulk and edge invariants for interacting, many-body localized Floquet systems in two spatial dimensions. This method is based on a general mathematical object which we call a flow. As an application of our method, we derive bulk invariants for Floquet systems without symmetry, as well as for systems with $U(1)$ symmetry. We also derive new formulations of previously known single-particle and many-body invariants. For bosonic systems without symmetry, our invariant gives a bulk counterpart of the rational-valued GNVW index $\frac{p}{q}$ quantifying transport of quantum information along the edge.