Gutzwiller Approximation in Degenerate Hubbard Models

Degenerate Hubbard models are studied using the Generalized-GutzwillerApproximation. It is found that the metal-insulator transition occurs at a finite correlation Uc when the average number of electrons per lattice site is an integer. The critical Uc depends sensitively on both the band degeneracy N and the filling x. A derivation is presented for the general expression of Uc(x,N) which reproduces all previously known Gutzwiller solutions, including that of the Boson Hubbard model. Effects of the lattice structure on the metal-insulator transition and the effective mass are discussed. PACS numbers: 71.10.+x,71.30.+h,74.70.W Typeset using REVTEX 1 The simple Hubbard model, where each lattice site is occupied by at most two electrons, has been extensively studied in recent years as a model of strongly correlated electron systems. But in many systems, such as molecular solids C60 and AxC60, 3 the conduction band is degenerate which allows the occupation of more than two electrons per lattice site. For these systems, studying the degenerate Hubbard model on a lattice is the first step toward the understanding of electron-electronic correlations. Yet, there has been little progress since the pioneering works of Chao and Gutzwiller in early 1970s. Recently, we succeeded in obtaining the Gutzwiller-like analytical solutions to degenerate Hubbard models using a scheme similar to the original Gutzwiller-Approximation. A brief report of our results has been published. The solution was used successfully to interpret the unusual metal-insulator transitions observed in fullerides AxC60. 6,7 In this paper we present details of our derivation and the approximation. In addition, effects of the crystal lattice structure on the metal-insulator transition and the effective mass are also investigated. We consider the N -fold degenerate Hubbard model defined on a lattice