BETHE APPROXIMATION SCHEME FOR ITINERANT ELECTRON-SYSTEMS

After reviewing the fermi-linearization approach to interacting electron systems, we propose here a refinement of the method based on the extension to itinerant ferminon systems of the philosophy of the Bethe-Peierls treatment of classical systems. We focus our attention on a Hubbard-like model, deriving a general self-consistent scheme which we solve explicitly in the simplest case. We obtain a rich phase-space, exhibiting in particular two phase transitions depending on the band filling. Among the results, we discuss in detail the local magnetic moment, by comparing the outcome of our scheme to some known numerical results in one and two dimensions respectively.