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

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