Interpolating self-energy of the infinite-dimensional Hubbard model: Modifying the iterative perturbation theory

We develop an analytical expression for the self-energy of the infinite-dimensional Hubbard model that is correct in a number of different limits. The approach represents a generalization of the iterative perturbation theory to arbitrary fillings. In the weak-coupling regime perturbation theory to second order in the interaction U is recovered. The theory is exact in the atomic limit. The high-energy behavior of the self-energy up to order 1/${\mathrm{E}}^{2}$ and thereby the first four moments of the spectral density are reproduced correctly. Referring to a standard strong-coupling moment method, we analyze the limit U->\ensuremath{\infty}. Different modifications of the approach are discussed and tested by comparing with the results of an exact diagonalization study.