Dynamical vertex approximation - a step beyond dynamical mean field   theory
  We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean field theory and long-range correlations beyond. It allows for example to describe (para-)magnons and weak localization effects in strongly correlated systems. As a first application, we study the interplay between nonlocal antiferromagnetic correlations and the strong local correlations emerging in the vicinity of a Mott-Hubbard transition. 
A. Toschi, A. A. Katanin, and K. Held