THE MOMENT SUM-RULE AND ITS CONSEQUENCES FOR FERROMAGNETISM IN THE HUBBARD-MODEL

The sum rule for the moments of the spectral density is discussed for the single-band Hubbard model. It is shown that respecting the sum rul e up to the order m =3 is conceptually important for a qualitatively c orrect description of the quasi-particle band structure in the strong- correlation regime. Different analytical approximations for the self-e nergy are analyzed with respect to their compatibility with the moment , sum rule. To estimate the practical usefulness of the sum rule, corr elation functions and dynamical quantities are determined. The results obtained within the various approximation schemes of different comple xity are compared with each other and also with essentially exact resu lts available for infinite-dimensional lattices. It turns out that the m = 3 moment is rather unimportant for the paramagnetic phase on the hyper-cubic lattice. Contrary, it decisively influences the magnetic p hase boundary as well as the critical temperature for the ferromagneti c phase on an fc.c.-type lattice.