On Mean Field Theories of Singlet Superconductivity in Extended Hubbard Models

Abstract

Hubbard models extended by attractive interactions between nearest neighbours have recently been discussed as models for heavy fermion superconductivity. Here, a comparison is carried through between mean field calculations at finite band width and exact results on ground state properties in the atomic limit (i.e. at zero band width). It turns out that the mean field approximation does not provide an appropriate description of the ground state of the system. This holds true for arbitrary band filling. For half-filled band, an extended mean field approximation is studied, allowing for both antiferromagnetism and (singlet) superconductivity. It is found that these two types of order do not coexist within mean field theory.