Time-dependent GW: Progress in Solving Kadanoff-Baym Equations with Dynamic GW Self Energy*

The ab initio GW plus Bethe-Salpeter equation (GW-BSE) approach has achieved great success in describing the linear absorption spectra of materials in equilibrium. However, many important photo-processes and experiments of interest that involve ultrafast and high-intensity pulses of light fall well outside the regime of equilibrium and linear responses. One can generalize the Green’s function formalism in many-body perturbation theory to nonequilibrium situations by solving the Kadanoff-Baym equations (KBE), but the presence of two time variables that need to be simultaneously evolved presents a significant computational challenge. In recent years, progress has been made in solving the KBE from ab initio in the static limit of the GW self energy, which greatly simplifies the time evolution. Here, we present progress on solving the KBE including dynamical effects in the self energy. We discuss time-evolution algorithms, memory effects, approximations to the dynamics, and convergence behavior.