Dynamical Vertex Approximation

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.

22 pages, 16 figures. Lecture notes published as: K. Held, "Dynamical vertex approximation", in E. Pavarini, E. Koch, D. Vollhardt, A. Lichtenstein (Eds.): "Autumn School on Correlated Electrons. DMFT at 25: Infinite Dimensions", Reihe Modeling and Simulation, Vol. 4 (Forschungszentrum Julich, 2014). ISBN 978-3-89336-953-9