Quenching the Hubbard Model: Comparison of Nonequilibrium Green's Function Methods

ABSTRACT We benchmark nonequilibrium Green's function (NEGF) approaches for interaction quenches in the half‐filled Fermi–Hubbard model in one and two dimensions. We compare fully self‐consistent two‐time Kadanoff–Baym equations (KBE), the generalized Kadanoff–Baym ansatz (GKBA), and the recently developed NEGF‐based quantum fluctuations approach (NEGF‐QF) with second‐order Born (2B) and GW self‐energies. As references, we use DMRG in 1D and time‐dependent perturbation theory at weak coupling. While all methods reproduce the early‐time build‐up of correlations (prethermalization), different deficiencies emerge during the slower relaxation in the long‐time limit: KBE shows overdamped oscillations, GKBA exhibits a negative overshoot of the Fermi‐surface jump, and NEGF‐QF develops a prethermalization plateau with delayed relaxation. In 1D, we find that GKBA + 2B agrees best with DMRG across the explored parameter range, while QF + GW deviates the most, consistent with its reduced self‐consistency. In 2D, all approaches correctly capture the momentum‐dependence of the relaxation dynamics.