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We explore the non-equilibrium dynamics of a one-dimensional Fermi-Hubbardsystem as a sensitive testbed for the capabilities of the time-dependenttwo-particle reduced density matrix (TD2RDM) theory to accurately describetime-dependent correlated systems. We follow the time evolution of theout-of-equilibrium finite-size Fermi-Hubbard model initialized by a quench overextended periods of time. By comparison with exact calculations for smallsystems and with matrix product state (MPS) calculations for larger systems butlimited to short times, we demonstrate that the TD2RDM theory can accuratelyaccount for the non-equilibrium dynamics in the regime from weak to moderatelystrong inter-particle correlations. We find that the quality of the approximatereconstruction of the three-particle cumulant (or correlation) required for theclosure of the equations of motion for the reduced density matrix is key to theaccuracy of the numerical TD2RDM results. We identify the size of thedynamically induced three-particle correlations and the amplitude of crosscorrelations between the two- and three-particle cumulants as criticalparameters that control the accuracy of the TD2RDM theory when currentstate-of-the art reconstruction functionals are employed.

Non-equilibrium correlation dynamics in the one-dimensional Fermi-Hubbard model: A testbed for the two-particle reduced density matrix theory