GW and beyond approaches to quasiparticle properties in metals

We perform a comparative study of the performances of some standard approaches within the many-body perturbation theory. We calculate quasiparticle dispersions, lifetimes, and spectral functions of aluminum and sodium. Calculations have been carried out in the GW approximation with a plasmon pole model (PPM) or with the contour deformation technique. We also accounted for vertex corrections either only in the screening (replacing the RPA dielectric function with the TDLDA or the Hubbard one) or both in the screening and in the self-energy (using the Del Sole et al. local vertex). Results show the failure of the PPM to describe the corrections far from the Fermi energy, as well as its inability to describe quasiparticle lifetimes and spectral functions. Calculations with a more refined screened interaction decrease the bandwidths and the lifetime of the quasiparticles compared with the GW as well as inducing tiny modifications in the spectral functions. The inclusion of the vertex also in the self-energy cancels the effects arising from the screening by pushing the results back toward the GW ones or even enlarging the differences.