Spectral properties of the interacting homogeneous electron gas from algorithmic inversion*

Despite its simplicity, the interacting homogeneous electron gas is a paradigmatic test case in the study of the electronic structure of condensed matter. Beside being a model for valence electrons in simple metals, it also provides the fundamental ingredients for
density-functional approximations. Here, we study it with many-body perturbation theory at different GW levels (one shot, partially self-consistent, and fully self-consistent). In order to do so, we introduce a novel numerical implementation of many-body perturbation theory that targets the full-frequency dependence of the Green's function and self-energy. We present results for a broad range of densities, with a special focus on the total energy, the density of states, and the spectral potential.