We propose an approach for the ab initio calculation of materials with strong electronic correlations which is based on all local (fully irreducible) vertex corrections beyond the bare Coulomb interaction. It includes the so-called GW and dynamical mean field theory and important non-local correlations beyond, with a computational effort estimated to be still manageable.
@article{arxiv.1104.2188,
title = {Ab initio calculations with the dynamical vertex approximation},
author = {A. Toschi and G. Rohringer and A. A. Katanin and K. Held},
journal= {arXiv preprint arXiv:1104.2188},
year = {2015}
}