  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.
