Emergent Spectral Features from Efficient Real-Time Simulations of Non-Equilibrium Green's Functions

Simulating non-equilibrium Green's functions is computationally intensive due to the need to capture dynamical many-body correlations in time. Conventional many-body perturbation approaches, such as the Kadanoff–Baym equations (KBE), scale cubically with the total number of time steps, making long-time simulations prohibitive. Here, we employ the recently developed Real-Time Dyson Expansion (RT-DE) method, which achieves linear scaling in time while retaining essential dynamical correlation effects. We apply RT-DE to the multi-band Hubbard model, exploring regimes from weak to strong coupling, and from short- to long-range interactions under various pulsed excitations forms. Our results reveal emergent spectral features, including peak splittings and satellite structures associated with excitonic features, which are absent in mean-field and standard KBE approaches. We also discuss the accuracy and limitations of RT-DE and its potential extension toward ab initio nonequilibrium simulations of materials.