Quasiparticle Self consistent GW with ladder diagrams in W

We present an extension of the quasiparticle self-consistent GW approximation (QSGW) 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. QSGW yields a good and consistent description of the electronic structure and optical response, but systematic errors in several properties appear, A primary object of this paper is to assess to what extent including ladder diagrams in W ameliorates systematic errors in the QSGW approximation: notably a tendency to overestimate insulating bandgaps, blue-shift plasmon peaks in the imaginary part of the dielectric function, and underestimate the dielectric constant. We find ladders do ameliorate shortcomings of QSGW in insulators to a remarkable degree, and provide a high fidelity description both the one-body Green's function and the dielectric function, for a wide range of insulators. Some discrepancies remain, we show to what extent the errors are systematic and can be traced to diagrams missing from the theory. Another finding of this work is to establish the distinction between the optical gap and fundamental gap in some commonly studied materials, such as SrTiO₃ and CuAlO₂.