Electronic structure of strongly correlated materials: From one-particle to many-body theory

One of the great challenges of modern condensed matter theory is to develop reliable and practical methods for describing the electronic structure of strongly correlated materials fully from first principles. It has been known for a long time that the widely used Kohn-Sham density functional theory within the local density approximation (LDA) often fails for these systems. This paper describes the theoretical development of including electron correlations beyond the LDA with emphasis on ab initio methods, starting from the highly successful LDA+U and the many-body Green's function-based GW method to the state-of-the-art combination of dynamical mean-field theory and GW. Apart from reviewing the development so far we also present some previously unpublished results.