Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner/Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting spins in an insulator. However many experimental studies, e.g. of (de)magnetization processes, focus on itinerant local-moment materials such as transition metals and various of their compounds. We here present a general theoretical framework that is capable of addressing correlated spin dynamics, also in the presence of a vanishing charge gap. A real-space implementation of the time-dependent rotational-invariant slave boson methodology allows to treat non-equilibrium spins numerically fast and efficiently beyond linear response as well as beyond the band-theoretical or Heisenberg limit.
