Dynamical vertex correction to the generalized Kadanoff-Baym Ansatz

The generalized Kadanoff-Baym Ansatz, used to simplify the non-equilibrium Green's functions to the kinetic equation for the density matrix, leads to an incorrect dynamics of a system if the self-energy has a rich energy spectrum. We propose an approximation of the vertex correction which dynamically changes with the density matrix while it benefits from simplicity of stationary propagators. On the molecular bridge between ferromagnetic leads, we demonstrate that this simple vertex fixes the failure of the kinetic equation on a negligible computational cost.