QSGW: Quasiparticle Self-Consistent GW with Ladder Diagrams in W: Article No. 165104

We present an extension of the quasiparticle self-consistent GW approximation (QSGW) [T. Kotani et al., Phys. Rev. B 76, 165106 (2007)] to include vertex corrections in the screened Coulomb interaction W. This is achieved by solving the Bethe-Salpeter equation for the polarization matrix at all k points in the Brillouin zone. We refer to this method as QSGW. QSGW yields a reasonable and consistent description of the electronic structure and optical response, but systematic errors in several properties appear, notably a tendency to overestimate insulating band gaps, blueshift plasmon peaks in the imaginary part of the dielectric function, and underestimate the dielectric constant ..epsilon..infinity... A primary objective of this paper is to assess to what extent including ladder diagrams in W ameliorates systematic errors for insulators in the QSGW approximation. For benchmarking we consider about 40 well-understood semiconductors, and also examine a variety of less well-characterized nonmagnetic systems, six antiferromagnetic oxides, and the ferrimagnet Fe3O4. We find ladders ameliorate shortcomings in QSGW to a remarkable degree in both the one-body Green's function and the dielectric function for a wide range of insulators. New discrepancies with experiment appear, and a key aim of this paper is to establish to what extent the errors are systematic and can be traced to diagrams missing from the theory. One key finding of this work is to establish a relation between the band gap and the dielectric constant ..epsilon..infinity... Good description of both properties together provides a much more robust benchmark than either alone. We show how this information can be used to improve our understanding of the one-particle spectral properties in materials systems such as SrTiO3 and FeO.