Strongly correlated Falicov-Kimball model in infinite dimensions

In this paper we have examined the strongly correlated Falicov-Kimball model in infinite dimensions with the help of a diagrammatic technique for the Hubbard X-operators. This model is represented by the simplified t-J model with introduced intra-atomic level energy epsilon(0) for localized particles. For the Bethe lattice with z --> infinity, we have found that the obtained equations for the band Green's function and self-energy coincide with the corresponding Brandt-Mielsch equations taken at U --> infinity, and are resolved in analytical form both in the homogeneous phase and in the chessboard phase. In the latter case we have obtained the equation for the order parameter defining the chessboard-like distribution of localized particles. Instability of the homogeneous phase and properties of the chessboard phase are investigated in detail. In particular, it is found that the temperature dependence of the chessboard order parameter has reentrant behaviour for some range of values of epsilon(0).