Alloy analog approach and the Gutzwiller approximation as particular cases of a mean-field theory

In this paper, the authors develop a new mean field-theory for systems with on-site correlations, like the Hubbard and Anderson models. It consists in a generalization of the saddle-point approximation to the functional integral representation proposed by Kotliar and Ruckenstein to more than one saddle point. It also contains the alloy analog approximation proposed by Hubbard as a particular case. For a half-filled Hubbard model and a model density of states appropriate for three dimensions, the authors obtain a metal to insulator transition as U increases. The effective Hamiltonian for the insulating phase contains two split bands (rather than only one with an extremely heavy mass) which reproduce correctly the Green's functions of the atomic limit