Emergence of hydrodynamics in large driven quantum systems

Many non-equilibrium dynamical properties of Floquet (driven) systems remain unclear. In particular, understanding the microscopic details of short-time thermalization as well as the cross-over to hydrodynamics and late-time Floquet heating remains an open challenge. We investigate the dynamics of Floquet systems using a novel numerical method termed 'density matrix truncation' (DMT). At small system sizes, we gauge the applicability and limitations of DMT via comparison with Krylov subspace methods; we demonstrate that DMT can capture both the prethermal state and the late-time thermalization to infinite temperature. Pushing DMT to larger system sizes (up to L = 100) enables us to confirm the exponential scaling of the Floquet heating time with driving frequency. Access to large systems allows us to directly study the emergence of late-time hydrodynamics. In particular, we implement a spatially inhomogeneous drive to probe the interplay between Floquet heating and the diffusion of local energy density. Despite the heating being a coherent quantum process, the emergent hydrodynamical behavior is captured by a simple classical diffusion equation.