Stability of the anomalous Floquet insulator

Many-body localization stabilizes periodically driven quantum systems, leading to the possibility of distinct non-equilibrium Floquet phases of matter with no equilibrium counterparts. Here we demonstrate the existence of an anomalous Floquet insulator (AFI) phase in two dimensions. This phase is characterized by a nonzero, quantized magnetization in the bulk, and delocalized chiral states at the edge that support a quantized net current. The phase is stabilized by disorder, and we argue that the bulk remains many-body localized in the presence of interactions, while the chiral edge states display protected thermalization. We numerically investigate the dynamics of AFI in an open geometry. We find that the non-uniform particle density profiles remain stable in the bulk, out to the longest timescales that we can access, while the propagating edge states persist and thermalize, despite being coupled to the localized bulk. This opens up the possibility of observing quantized edge transport at high temperature, in the presence of interactions.