9 S ep 1 99 8 Optimization of alloy - analogy - based approaches to the infinite - dimensional Hubbard model

An analytical expression for the self-energy of the infinite-dimensional Hubbard model is proposed that interpolates between different exactly solvable limits. We profit by the combination of two recent approaches that are based on the alloy-analogy (Hubbard-III) solution: The modified alloy-analogy (MAA) which focuses on the strong-coupling regime, and the Edwards-Hertz approach (EHA) which correctly recovers the weak-coupling regime. Investigating the high-energy expansion of the EHA self-energy, it turns out that the EHA reproduces the first three exactly known moments of the spectral density only. This may be insufficient for the investigation of spontaneous magnetism. The analysis of the high-energy behavior of the CPA self-consistency equation allows for a new interpretation of the MAA: The MAA is the only (two-component) alloy-analogy that correctly takes into account the first four moments of the spectral density. For small U , however, the MAA does not reproduce Fermi-liquid properties. The defects of the MAA as well as of the EHA are avoided in the new approach. We discuss the prospects of the theory and present numerical results in comparison with essentially exact quantum Monte Carlo data. The correct high-energy behavior of the self-energy is proved to be a decisive ingredient for a reliable description of spontaneous magnetism.