Total energy from the Galitskii-Migdal formula using realistic spectral functions

Although many-body perturbation theory (MBPT) for quite some time has been used to determine quasiparticle energies and optical properties of solids, traditionally the issue of ground-state energy has not been addressed with this method. Rather, most efforts in that direction have been concentrating on various mean-field theories. The success of density-functional theory (DFT) has enhanced this evolution. However, there are certain systems for which known approximations for the so-called exchange-correlation potential within DFT cannot correctly reproduce the observed ground states or the calculated ground-state properties deviate significantly from experiment. In situations like these, an alternative is to have a theory that does not depend on such approximations, but rather is derived from first principles within MBPT, albeit with some other form of approximation. We here investigate two such schemes, rather closely related to each other, in order to highlight the essential properties of a MBPT that correctly describes spectral properties and ground-state energies. As a first step, we have investigated the case of the electron gas that provides a starting point for more general cases of real materials.