Many-body perturbation theory for quasiparticle energies

Abstract

Quasiparticle energies are defined as ionization potentials (IP) for occupied orbitals and as electron affinities (EA) for unoccupied orbitals. They correspond to band energies in extended systems. As many-body perturbation theory (MBPT) readily provides energies of any order, we extend the theory to give any order corrections to IPs and EAs for finite and infinite systems, which permits a direct evaluation of correlation corrections. The diagrams for IPs and EAs can be classified into two types. The first type are linked diagrams which can be further separated into two sets. One set consists of the diagrams having one and only one bubble with a fixed index. They mainly account for orbital relaxation effects that are shown to have a finite contribution in infinite periodic systems. The other diagrams are derived from the diagrams for the total energy. In each of those diagrams, there is one and only one line with a fixed index. The second type of diagrams are the diagrams which have two or more lines with fixed indices. Because of mutual cancellations among the contributions of the orbital relaxation and electron correlation, the only remaining diagrams are those which fall apart by switching any two ending vertices of the lines that have fixed indices. These diagrams can be expressed as unlinked diagrams, of which each separated part is a diagram of the first type. Since each unlinked part has one line with a fixed index, these unlinked diagrams are size intensive. The rules to interpret these diagrams are explained. The connection between the first type of diagrams for the MBPT correction and the total self-energy with the diagonal approximation for E=εp(0) in propagator or Greens function methods is explicitly established for any order.