Flow Renormalization and Prethermal Regimes of Periodically-Driven Quantum Systems

One of the most fascinating aspects of non-equilibrium physics is that a quantum system pushed out of equilibrium can exhibit markedly different dynamics when probed on different time scales. We develop a flow renormalization approach for periodically-driven quantum systems, for which a rigorous relation between "flow time" and real time can be established. In this formalism, the dynamical problem is recast in terms of a flow towards an attractive thermal fixed point, while narrowly avoiding a series of unstable fixed points that determine distinct transient dynamical regimes at intermediate times. We show that a unique choice of flow permits relating flow-time and real-time evolution via analytic continuation, and study the appearance of long-lived prethermal regimes in Floquet Hubbard models and spin chains.