SOME PROPERTIES OF THE POSITIVE-U AND NEGATIVE-U HUBBARD MODEL

Abstract

In this article we review the properties of the 2D Hubbard model by considering at the same time the cases of repulsive and attractive interaction. The paramagnetic solution is studied by means of the composite operator method in the static approximation for the case of half-filling. Some properties of the two models, as the double occupancy and the spin magnetic susceptibility, are calculated for various values of interaction and temperature and compared. In particular, the different role played by thermal fluctuations is analyzed. Analytical and numerical calculations show that there is a critical value of the interaction, Uc, where the system exhibits a metal-insulator transition. At zero temperature it is found that Uc=−W for the negative-U model and Uc≈1.68W for the positive-U model, where W is the band width. At zero temperature, when the strength of the attractive interaction equals the band width, the system exhibits a phase transition to a pair state, where all the electrons are locally paired. The temperature Tp which controls the crossover to the pair state is calculated as a function of U. For strong attractive interaction χ0 is strongly depressed; increases by increasing T and tends to zero as T→TP.