The nonequilibrium dynamics of strongly-correlated fermions in lattice systems have attracted considerable interest in the condensed matter and ultracold atomic-gas communities. While experiments have made remarkable progress in recent years, there remains a need for the further development of theoretical tools that can account for both the nonequilibrium conditions and strong correlations. For instance, time-dependent theoretical quantum approaches based on the density matrix renormalization group (DMRG) methods have been primarily applied to one-dimensional setups. Recently, two-dimensional quantum simulations of the expansion of fermions based on nonequilibrium Green functions (NEGF) have been presented [Schluenzen et al., Phys. Rev. B 93, 035107 (2016)] that showed excellent agreement with the experiments. Here we present an extensive comparison of the NEGF approach to numerically accurate DMRG results. The results indicate that NEGF are a reliable theoretical tool for weak to intermediate coupling strengths in arbitrary dimensions and make long simulations possible. This is complementary to DMRG simulations which are particularly efficient at strong coupling.
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