Electron-magnon dynamics triggered by an ultrashort laser pulse: A real-time Dual $GW$ study

Ultrafast irradiation of correlated electronic systems triggers complex dynamics involving quasi-particle excitations, doublons, charge carriers, and spin fluctuations. To describe these effects, we develop an efficient non-equilibrium approach, dubbed D-$GW$, that enables a self-consistent treatment of local correlations within dynamical mean-field theory (DMFT) and spatial charge and spin fluctuations, that are accounted for simultaneously within a diagrammatic framework. The method is formulated in the real-time domain and provides direct access to single- and two-particle momentum- and energy-dependent response functions without the need for analytical continuation, which is required in Matsubara frequency-based approaches. We apply the D-$GW$ method to investigate the dynamics of a photo-excited extended Hubbard model, the minimal system that simultaneously hosts strong charge and spin fluctuations. Focusing on the challenging parameter regime near the Mott transition, we demonstrate that correlated metals and narrow-gap Mott insulators undergo distinct thermalization processes involving complex energy transfer between single-particle and collective electronic excitations.