Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps.

Topological phenomena in periodically driven, isolated quantum many body systems are difficult to obtain due to the generic tendency of such systems to heat up towards a maximum entropy state in the long time limit. Here we investigate a mechanism to transiently stabilize topological phenomena over a long-time window, for systems driven at low frequencies. This mechanism provides a route for obtaining long-lived prethermal states with anomalous topological properties, unattainable in equilibrium. We consider the dynamics of interacting particles in a slowly driven lattice with two (or more) bands separated by a bandgap. In the case where the bandgap of the Hamiltonian at any specific time is large we obtain an analytical bound for the rate of change in the number of particles populating these bands. 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 prethermal time window, this leads to the existence of a quasi-steady state which is characterized by maximum entropy subject to the constraint of fixed number of particles in each band. By initializing the system with a majority of particles in one of the bands, the topological properties of the bands can be measured. For example, this mechanism can be used to obtain quasi-steady states in slowly driven one dimensional systems which carry universal currents, or quasi-steady states of drive-induced Weyl points in 3-dimensional systems.