The real-time Dyson expansion: many-body physics with mean-field cost

Time-resolved photoemission spectroscopy is the key technique to probe the real-time non-equilibrium dynamics of electronic states. However its theoretical prediction remains a challenge. Typically including many-body correlations (crucial for accurate predictions of non-equilibrium phenomena), requires solving the Kadanoff-Baym equations, which scale cubically in the number of time-steps. This poor scaling makes them prohibitively expensive in many practical situations. In a recent paper we have introduced a new method, called the RT-DE, that allows for the inclusion of dynamical correlations in the spectral function while maintaining the same scaling in the number of time steps as for mean-field approaches (effectively linear). In this talk we will introduce the RT-DE methodology and then discuss an application studying the effect of dynamical correlations on band-gap renormalization in photo-excited semiconductors.