Multiple electron-hole scattering effect on quasiparticle properties in a homogeneous electron gas

We present a detailed study of a contribution of the T matrix accounting for multiple scattering between an electron and a hole to the quasiparticle self-energy. This contribution is considered as an additional term to the GW self-energy. The study is based on a variational solution of the T-matrix integral equation within a local approximation. A key quantity of such a solution, the local electron-hole interaction, is obtained at the small four-momentum transfer limit. Performed by making use of this limit form, extensive calculations of quasiparticle properties in the homogeneous electron gas over a broad range of electron densities are reported. We carry out an analysis of how the T-matrix contribution affects the quasiparticle damping rate, the quasiparticle energy, the renormalization constant, and the effective mass enhancement. We find that in comparison with the GW approximation the inclusion of the T matrix leads to an essential increase of the damping rate, a slight reduction of the GW band narrowing, a decrease of the renormalization constant at the Fermi wave vector, and some "weighting" of quasiparticles at the Fermi surface.