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Ultra-fast photo-carrier relaxation in Mott insulators with short-range spin correlations

We compute the time-resolved photoemission spectrum after photo-doping in a two-dimensional Mott-Hubbard insulator. We find that the relaxation rate of high-energy photo-doped electrons in the paramagnetic phase scales with the strength of the nearest-neighbor spin correlations, which implies a pronounced increase of the relaxation times with temperature and excitation density. Finite doping, in contrast, opens additional scattering channels and leads to a faster relaxation. To obtain our results we have implemented a nonequilibrium version of the dynamical cluster approximation (DCA), which, in contrast to single-site dynamical mean-field theory, captures the effect of short-range correlations.