Ab initio many-body treatment of the electronicstructure of metals

We propose and apply a combination of an ab initio (band-structure) calculation with a many-body treatment including screening effects. We start from a linearized muffin-tin orbital (LMTO) calculation to determine the Bloch functions for the Hartree one-particle Hamiltonian, from which we calculate the static susceptibility and dielectric function within the standard random phase approximation (RPA). From the Bloch functions we obtain maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and unscreened and screened Coulomb matrix elements are calculated. This yields a multi-band Hamiltonian in second quantization with ab initio parameters, for which screening has been taken into account within the simplest standard approximation. Then, established methods of many-body theory are used. We apply this concept to a simple metal, namely lithium (Li). Here the maximally localized Wannier functions turn out to be of the sp³-orbital kind. Furthermore, only the on-site contributions of the screened Coulomb matrix elements are relevant, and a generalized, four-band Hubbard model is justified. The screened on-site Coulomb matrix elements are considerably smaller than the band width because of which it is sufficient to calculate the selfenergy in weak-coupling approximation. We compare results obtained within the screened Hartree-Fock approximation (HFA) and within the second-order perturbation theory (SOPT) in the Coulomb matrix elements for Li and find that many-body effects are small but not negligible even for this simple metal.