A finite electric-field approach to evaluate the vertex correction for the screened Coulomb interaction in the quasiparticle self-consistent GW method.

We apply the quasiparticle self-consistent GW method (QSGW) to slab models of ionic materials, LiF, KF, NaCl, MgO, and CaO, under electric field. Calculated optical dielectric constants {\epsilon}{\infty}(Slab) show very good agreements with experiments. For example, we have {\epsilon}{\infty}(Slab)=2.91 for MgO, in agreement with the experimental value {\epsilon}{\infty}(Experiment)=2.96, whereas we have {\epsilon}{\infty}(RPA)=2.37 in the random-phase approximation for the bulk MgO. The large discrepancy 2.91-2.37 is due to the vertex correction. Our result gives a rationale for methods such as QSGW80 [Deguchi et al., doi:10.7567/JJAP.55.051201].