Gutzwiller approximation in degenerate Hubbard models

The details of the Generalized-Gutzwiller-Approximation in degenerate Hubbard models are presented. It is found that the metal-insulator transition occurs at a finite correlation U-c when the average number of electrons per lattice site is an integer. A derivation is given for the general expression of U-c(x, N) which reproduces all previously known Gutzwiller solutions, including that of the boson Hubbard model. The U-c depends sensitively on both the band degeneracy N and the filling x. Effects of the lattice structure on the metal-insulator transition and the effective mass are discussed.