Correlated Electron Dynamics in Finite Hubbard Clusters: Benchmarking the G1–G2 Scheme

The selfconsistent theoretical treatment of correlation and quantum effects beyond one-dimensional systems is a particular challenge that has been successfully attacked with nonequilibrium Green functions (NEGF) methods [1]. However, NEGF simulations are hampered by a cubic scaling of the computation time with the number of time steps N_t. Recently, a dramatic acceleration has been achieved within the G1–G2 scheme [2] by transforming the NEGF equations, within the Hartree-Fock GKBA, to a time local form for the single-particle and two-particle Green functions. A detailed discussion of the method, its application to a variety of selfenergies including particle-particle and particle-hole T-matrix approximation, GW approximation, and dynamically screened ladder approximation was presented recently [3]. Here, we present extensive tests of the G1–G2 scheme within the screened ladder approximation for finite Hubbard clusters out of equilibrium. Stable simulations over long times are achieved by enforcing contraction consistency and by performing a purification of the dynamics [4].

[1] N. Schlünzen et al., PRB 93, 035107 (2016)

[2] N. Schlünzen et al., PRL 124, 076601 (2020)

[3] J.-P. Joost et al., PRB 101, 245101 (2020)

[4] F. Lackner et al., PRA 91, 023412 (2015)