Approximative treatment of 5f-systems with partial localization due to intra-atomic correlations

Increasing experimental and theoretical evidence points towards a dual nature of the 5f electrons in actinide-based strongly correlated metallic compounds, with some 5f electrons being localized and others delocalized. In a recent paper [Phys. Rev. B 69, 115114 (2004)], we suggested the interplay of intra-atomic correlations as described by Hund's rules and a weakly anisotropic hopping (hybridization) as a possible mechanism. The purpose of the present work is to provide a step towards a microscopic description of partial localization in solids by analyzing how well various approximation schemes perform when applied to small clusters. It is found that many aspects of partial localization are described appropriately both by a variational wave function of Gutzwiller type and by a treatment which keeps only those interactions which are present in so-called LDA+U calculations. In contrast, the energies and phase diagram calculated within the Hartree-Fock approximation show little resemblance with the exact results. Enhancement of hopping anisotropy by Hund's rule correlations is found in all approximations.