Tracing the Successes and Failures of the HF-GKBA in Non-equilibrium Systems

The Kadanoff-Baym equations (KBE) are a formally exact set of equations (provided that the exact self-energy is known) for the propagation of non-equilibrium Green's functions (NEGF). However, KBE suffers from poor numerical scaling with the system size and the simulation time. Practical calculations thus often resort to the approximate Hartree-Fock generalized Kadanoff-Baym ansatz (HF-GKBA). However, comparison of HF-GKBA with exact or KBE results shows good agreement only for relatively short times, but such direct comparison has been limited to a limited set of problems: simple two band models with onsite interactions. I will show that the highly restricted models are partly to blame for the poor performance of HF-GKBA. We study several classes of non-equilibrium systems with long-range interactions and various forms of non-equilibrium state preparation. Further, we will demonstrate under which conditions the non-equilibrium dynamics is amenable to efficient numerical approximations that can further reduce the computational cost. This work outlines the reliability of HF-GKBA for studying realistic non-equilibrium systems fully from first-principles.