Ab initio dynamical vertex approximation

Abstract

Diagrammatic extensions of dynamical mean field theory (DMFT) such as the dynamical vertex approximation (DΓA) allow us to include non-local correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an AbinitioDΓA approach for electronic structure calculations of materials. Starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare non-local Coulomb interaction and all local vertex corrections. From this we calculate the full non-local vertex and the non-local self-energy through the Bethe-Salpeter equation. The AbinitioDΓA approach naturally generates all local DMFT correlations and all non-local GW contributions, but also further non-local correlations beyond: mixed terms of the former two and non-local spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3. arXiv:1610.02998v2 [cond-mat.str-el]

Towards ab initio Calculations with the Dynamical Vertex Approximation

“…Grey lines only denote the incoming and outgoing frequencies and momenta, whereas black lines denote internal propagators G. Please note that we have adjusted the index convention to the one in Ref. 86 which is slightly different from Refs. 84, 87. tion.…”

“…81,83) For a review see. 84) For ab initio materials calculations, it has been suggested 85,86) to use as a starting vertex Γ q the bare non-local Coulomb interaction V q as well as all local vertex corrections Γ loc , which also includes the local Coulomb (Hubbard) interaction U. This way all GW diagrams and all local DMFT correlations are generated, but also non-local correlations beyond, such as spin fluctuations.…”

“…AbinitioDΓA has been recently implemented and applied to study non-local correlations in SrVO 3 . 86) In this paper we review the AbinitioDΓA method as well as the recent progress for calculating the multi-orbital local vertex. In Section 2, we introduce the multi-orbital Hamiltonian that we want to solve and our notation regarding Green's functions and vertices.…”

“…Section 3 is devoted to the continuoustime quantum Monte Carlo calculation (CT-QMC) of the local two-particle vertex, using vertex asymptotics 87) and worm sampling. 88) In Section 4, we recapitulate the AbinitioDΓA algorithm 86,89) which starts with the local vertex plus the bare non-local interaction, constructs through the Bethe-Salpeter equation the non-local full vertex and through the SchwingerDyson equation the non-local self-energy. In Section 5, we present the results obtained for SrVO 3 and (beyond Ref.…”

“…In Section 5, we present the results obtained for SrVO 3 and (beyond Ref. 86) the difference in self-energy when using the vertex asymptotics in CT-QMC. Finally we provide a summary and outlook in Section 6.…”