Fast Nonequilibrium Green Functions simulations with GW selfenergies

Quantum kinetic approaches [1] have proven successful in describing dynamics of the uniform electron gas. The Nonequilibrium Green Functions (NEGF) method is a powerful tool to compute time-dependent expectation values of single-particle observables in correlated quantum many-body-systems. Its unfavorable N_t³ scaling with propagation time N_t could be reduced to N_t² by introduction of the Generalized Kadanoff-Baym Ansatz (GKBA)[2]. Recently, an exact time-local (N_t¹) reformulation of the GKBA, the G1–G2 scheme [3,4], has been found for various self energies, which makes this method viable for long time simulations.
In the Jellium basis the G1–G2 scheme has an especially advantageous CPU time scaling of N_b³N_t¹ for both second-order and GW selfenergies, which makes this approach particularly interesting for this system. Furthermore, its derivation gives rise to an alternative way to compute the nonequilibrium screened potential. Here, we present first relaxation results in 1 and 2 dimensions.
[1] M. Bonitz, Quantum Kinetic Theory (Springer, 2016)
[2] P. Lipavský, V. Špička, B. Velický, Phys. Rev. B34, 6933 (1986)
[3] N. Schlünzen, J.-P. Joost, M. Bonitz, Phys. Rev. Lett. 124, 076601 (2020)
[4] J.-P. Joost, N. Schlünzen, M. Bonitz, Phys. Rev. B 101, 245101 (2020)