Prethermalization and topological transport in slowly driven Floquet systems

Topological phenomena in periodically driven quantum many body systems are difficult to obtain due to the generic tendency of such systems to heat up and tend towards an infinite temperature-like state. We investigate a mechanism to transiently stabilize topological phenomena over a long-time window for systems driven at low frequencies. We derive an analytical bound for the rate of change in the number of particles populating the Floquet bands of the system. The bound is exponentially small in the ratio between the instantaneous bandgap and the maximum between the driving frequency, interaction strength, and the bandwidth. Within the resulting prethermal time window, a quasi-steady state is stabilized, characterized by maximum entropy density subject to the constraint of fixed number of particles in each band. This mechanism provides a route for obtaining long-lived prethermal states with anomalous topological properties, unattainable in equilibrium, such as universal chiral currents in one dimension and magnetoelectric transport in three dimensions.