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We extend an approximation earlier developed by us for the single-impurityAnderson model to a full-size impurity solver for models of interactingelectrons with multiple orbitals. The approximation is based on parquetequations simplified by separating small and large energy fluctuationsjustified in the critical region of a pole in the two-particle vertex. We showthat an $l$-orbital model with most general interaction is described withinthis approximation by $4l^{2}\times 4l^{2}$ matrices and is Fermi liquid in themetallic phase. We explicitly calculate properties of a paramagnetic solutionof a two-orbital Hubbard model with a Hund exchange and orbital splittingwithin the dynamical mean-field approximation. We trace the genesis of ametal-insulator transition induced by a crystal field and vanishing of theKondo quasiparticle peak in strongly correlated orbitally asymmetric systems.

Multi-orbital simplified parquet equations for strongly correlated electrons