<i>Ab initio</i> dynamical vertex approximation

Abstract

Diagrammatic extensions of dynamical mean-field theory (DMFT) such as the dynamical vertex approximation $(\text{D}\mathrm{\ensuremath{\Gamma}}\text{A})$ allow us to include nonlocal correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an Ab initio $\text{D}\mathrm{\ensuremath{\Gamma}}\text{A}$ approach (Abinitio$\text{D}\mathrm{\ensuremath{\Gamma}}\text{A}$) for electronic structure calculations of materials. The starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare nonlocal Coulomb interaction and all local vertex corrections. From this, we calculate the full nonlocal vertex and the nonlocal self-energy through the Bethe-Salpeter equation. The Abinitio$\text{D}\mathrm{\ensuremath{\Gamma}}\text{A}$ approach naturally generates all local DMFT correlations and all nonlocal $GW$ contributions, but also further nonlocal correlations beyond: mixed terms of the former two and nonlocal spin fluctuations. We apply this new methodology to the prototypical correlated metal ${\text{SrVO}}_{3}$.