Dynamical Vertex Approximation

TL;DR

The paper introduces the dynamical vertex approximation, a method extending dynamical mean field theory to include non-local correlations, with applications to the Hubbard model and benchmark results on a benzene ring.

Contribution

It presents an elementary introduction to the dynamical vertex approximation and discusses recent advances and applications in strongly correlated electron systems.

Findings

Benchmark results for a benzene Hubbard ring demonstrate the method's accuracy.

Calculation of critical exponents for the 3D Hubbard model.

Long-range antiferromagnetic correlations can shift the Mott transition to zero interaction.

Abstract

Dynamical vertex approximation is a Feynman diagrammatic extension of dynamical mean field theory, including non-local correlations on all time and length scales. Starting with the Dyson and the parquet equations, the lecture notes give an elementary introduction to the dynamical vertex approximation. As a benchmark, results for an exactly solvable benzene Hubbard ring are presented. Recent highlights, the calculation of the critical exponents of the Hubbard model in 3D and that long-range antiferromagnetic correlations in 2D actually shift the (paramagnetic) Mott transition to interaction U=0, are reviewed.