Rotationally invariant parametrization of Coulomb interactions in multi-orbital Hubbard models

Multi-orbital models with strong Coulomb correlations represent a fundamental tool for the analysis of transition metal oxides, which exhibit physical properties strongly affected by the orbital degrees of freedom. In this context, specific relations between the local coupling constants must be imposed in order to preserve spin and charge rotational invariance. We present here an alternative route for the derivation of these relations, based on the use of a complete set of commuting operators which includes the pseudospin orbital operator and thus is particularly suited for the study of systems where phenomena of orbital ordering are known to play a major role. This approach is expected to be useful in investigations of multi-orbital Hubbard models analyzed within the framework of the dynamical mean field theory or in exact diagonalization studies on finite-size clusters.