Photoinduced dynamics of organic molecules using nonequilibrium Greens functions with second-Born, $GW$, $T$-matrix and three-particle ladder correlations

The ultrafast hole dynamics triggered by the photoexcitation of molecular targets is a highly correlated process even for those systems, like organic molecules, having a weakly correlated ground state. We here provide a unifying framework and a numerically efficient matrix formulation of state-of-the-art non-equilibrium Greens function (NEGF) methods like second-Born as well as $GW$ and $T$-matrix without and {em with} exchange diagrams. Numerical simulations are presented for a paradigmatic, exactly solvable molecular system and the shortcomings of the established NEGF methods are highlighted. We then develop a NEGF scheme based on the Faddeev treatment of three-particle correlations; the exceptional improvement over established methods is explained and demonstrated. The Faddeev NEGF scheme scales linearly with the maximum propagation time, thereby opening prospects for femtosecond simulations of large molecules.