Landau's theory of phase transitions provides a framework for describing phases of matter in thermodynamic equilibrium. Recently, an intriguing new class of quantum many-body localized (MBL) systems that do not reach thermodynamic equilibrium was discovered. The possibility of MBL systems to not heat up under periodic driving, which drastically changes the nature of dynamics in the system, opens the door for new, truly nonequilibrium phases of matter. In this paper we find a two-dimensional nonequilibrium topological phase, the anomalous Floquet insulator (AFI), which arises from the combination of periodic driving and MBL. Having no counterpart in equilibrium, the AFI is characterized by an MBL bulk, and topologically protected delocalized (thermalizing) chiral states at its boundaries. After establishing the regime of stability of the AFI phase in a simple yet experimentally realistic model, we investigate the interplay between the thermalizing edge and the localized bulk via numerical simulations of an AFI in a geometry with edges. We find that nonuniform particle density profiles remain stable in the bulk up to the longest timescales that we can access, while the propagating edge states persist and thermalize. These findings open the possibility of observing quantized edge transport in interacting systems at high temperature.

• Received 15 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.195133