Investigating the GW self-energy of the homogeneous electron gas in real space

Sammanfattning: The real space behavior of the GW self-energy in the electron gas model was investigated in this thesis work. The self-energy is naturally decomposed into the screened-exchange and the Coulomb-hole components. The self-energy calculated with different electron densities as function of frequency and position was compared with the static approximation. At low frequency, the screened-exchange self-energy is highly localized and can be well approximated by the static approximation. It can also be well approximated by an exchange potential with a Yukawa interaction characterized in range by the Fermi momentum. The Coulomb-hole self-energy shows a strong dependence on frequency and can be repulsive over a certain region of space at low density. The total self-energy is localized within the Wigner-Seitz radius and the degree of localization increases with decreasing density. The results of the present work may serve as a guidance for constructing an approximate self-energy in real materials.