Spectral Artifacts in Non-Equilibrium Green's Functions: A Comparative Study

The non-equilibrium Green's function method provides a powerful framework for studying time-dependent phenomena in interacting quantum systems as they pertain to experimental observables. Here we calculate the time-resolved ARPES spectra of a multiband Hubbard model driven out of equilibrium. We explore the dynamics using various formalisms within many-body perturbation theory, including the Kadanoff-Baym equations, exact diagonalization, real-time Dyson expansion, the generalized Kadanoff-Baym Ansatz, and time-dependent Hartree-Fock. We analyze the time off-diagonal components of the Green's functions and their role in resolving electronic excitations in the spectral functions. We find that the KBE formalism introduces artificial damping in the Green's function, effectively truncating the time off-diagonal correlations. As a result, the KBE spectral features are broadened such that excitonic peaks and other fine structure are obscured. In contrast, limiting the memory effects in KBE leads to improved spectral predictions.