Flow Renormalization and Emergent Prethermal Regimes of Periodically-Driven Quantum Systems

Abstract: We develop a flow renormalization approach for periodically-driven quantum systems, which reveals prethermal dynamical regimes and associated timescales via direct correspondence between real time and flow time behavior. In this formalism, the dynamical problem is recast in terms of coupling constants of the theory flowing towards an attractive fixed point that represents the thermal Floquet Hamiltonian at long times, while narrowly avoiding a series of unstable fixed points which determine distinct prethermal regimes at intermediate times. We study a class of relevant perturbations that trigger the onset of heating and thermalization, and demonstrate that the renormalization flow has an elegant representation in terms of a flow of matrix product operators. Our results permit microscopic calculations of the emergence of distinct dynamical regimes directly in the thermodynamic limit in an efficient manner, establishing a new computational tool for driven non-equilibrium systems.