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

physical review. b./physical review. b

Nonequilibrium dynamics in the one-dimensional Fermi-Hubbard model: A  comparison of the nonequilibrium Green functions approach and the density  matrix renormalization group method