Accurate band gaps of extended systems via efficient vertex corrections in GW

We propose the use of an approximate bootstrap exchange-correlation kernel to account for vertex corrections in self-consistent GW calculations. We show that the approximate kernel gives accurate band gaps for a variety of extended systems, including simple sp semiconductors, wide band-gap insulators, and transition-metal compounds with either closed or open d shells. The accuracy is comparable with that obtained via the solution of the Bethe-Salpeter equation but only at a fraction of the computational cost.