Carolyn Zhang (U. Chicago)
Bulk and edge signatures of interacting Floquet systems
 
In many examples of topological phases, there exists a bulk-boundary correspondence that relates topological invariants computed in the edge of the system to topological invariants computed in the bulk of the system. Periodically driven (Floquet) systems that are stabilized by many-body localization can also realize topological phases, some of which have no stationary analogue. It is expected that there also exists a bulk boundary correspondence in these kinds of systems. However, in most cases, only edge invariants have been obtained, and it was not known how, in general, to obtain topological invariants that one can compute in the bulk. In this talk, we present a bulk-boundary correspondence for single-particle and many-body Floquet systems in two spatial dimensions. Our correspondence is based on a general mathematical object that we call a ``flow," and we give concrete recipes for obtaining edge and bulk invariants from a given flow. In particular, we derive bulk invariants for several classes of Floquet systems, including interacting systems without symmetry and with U(1) symmetry. The bulk invariants do not require translation symmetry or flux threading. In systems with $U(1)$ symmetry, the bulk invariant can be related to both a magnetization density and a conserved edge current.