OPTIMIZATION OF ALLOY-ANALOGY-BASED APPROACHES TO THE INFINITE-DIMENSIONAL HUBBARD-MODEL

An analytical expression for the self-energy of the infinite-dimension al Hubbard model is proposed that interpolates between different exact ly solvable limits. We profit by the combination of two recent approac hes that are based on the alloy-analogy (Hubbard-III) solution: the mo dified alloy-analogy (MAA) which focuses on the strong-coupling regime , and the Edwards-Hertz approach (EIIA) which correctly recovers the w eak-coupling regime. Investigating the high-energy expansion of the EH A self-energy, it turns out that the EHA reproduces the first three ex actly known moments of the spectral density only. This may be insuffic ient for the investigation of spontaneous magnetism. The analysis of t he high-energy behavior of the CPA self-consistency equation allows fo r a new interpretation of the MAA: the MAA is the only (two-component) alloy-analogy that correctly takes into account the first four moment s of the spectral density. For small U, however, the MAA does not repr oduce Fermi-liquid properties. The defects of the MAA as well as of th e EHA are avoided in the new approach. We discuss the prospects of the theory and present numerical results in comparison with essentially e xact quantum Monte-Carlo data. The correct high-energy behavior of the self-energy is proved to be a decisive ingredient for a reliable desc ription of spontaneous magnetism.