Towards ab initio calculations with the dynamical vertex approximation

TL;DR

This paper reviews recent advances in diagrammatic extensions of dynamical mean-field theory, focusing on the ab initio dynamical vertex approximation (AbinitioDΓA) and its application to correlated materials like SrVO3.

Contribution

It introduces the ab initio dynamical vertex approximation and discusses algorithmic improvements for calculating two-particle quantities in materials.

Findings

Demonstrated potential of AbinitioDΓA with results on SrVO3

Improved quantum Monte Carlo algorithms for vertex calculations

Clarified the role of non-local fluctuations in correlated materials

Abstract

While key effects of the many-body problem---such as Kondo and Mott physics---can be understood in terms of on-site correlations, non-local fluctuations of charge, spin, and pairing amplitudes are at the heart of the most fascinating and unresolved phenomena in condensed matter physics. Here, we review recent progress in diagrammatic extensions to dynamical mean-field theory for ab initio materials calculations. We first recapitulate the quantum field theoretical background behind the two-particle vertex. Next we discuss latest algorithmic advances in quantum Monte Carlo simulations for calculating such two-particle quantities using worm sampling and vertex asymptotics, before giving an introduction to the ab initio dynamical vertex approximation (AbinitioD$\Gamma$A). Finally, we highlight the potential of AbinitioD$\Gamma$A by detailing results for the prototypical correlated metal SrVO$_3$.