Coulomb Correlations in 4d and 5d Oxides from First Principles - or How Spin-Orbit Materials choose their Effective Orbital Degeneracies

The interplay of spin-orbit interactions and Coulomb correlations has become a hot topic in condensed matter theory. Here, we review recent advances in dynamical mean-field theory-based electronic structure calculations for iridates and rhodates. We stress the notion of the effective degeneracy of the compounds, which introduces an additional axis into the conventional picture of a phase diagram based on filling and on the ratio of interactions to bandwidth.