Spectra and total energies from self-consistent many-body perturbation theory

With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GW approximation with those from an extended GWΓ scheme that includes a nontrivial vertex function and the fundamentally distinct Bethe-Goldstone approach based on the T matrix. The self-consistent Green’s function G, as derived from Dyson’s equation, is used not only in the self-energy but also to construct the screened interaction W for a model system. For all approximations we observe a similar deterioration of the spectrum, which is not removed by vertex corrections. In particular, satellite peaks are systematically broadened and move closer to the chemical potential. The corresponding total energies are universally raised, independent of the system parameters. Our results, therefore, suggest that any improvement in total energy due to self-consistency, such as for the electron gas in the GW approximation, may be fortuitous.