Dynamically enriched topological orders in driven two-dimensional systems

Time-periodic driving enables new nonequilibrium quantum phases of matter with topologically protected and quantum coherent motion that would be forbidden in thermal equilibrium. This work uncovers two new classes of driven topological phases in driven two-dimensional spin systems: i) Floquet symmetry protected topological phases, which are driven and interacting analogs of topological insulators whose edge states are protected against disorder and localization; and ii) Floquet enriched topological orders, in which time-dependent driving ``breaks'' the spins into anyonic particles with fractional statistics and oscillating topological charge. The physics of these phases is explored by constructing toy models that can be explicitly solved despite the presence of strong interactions.