VARIATIONAL PAIR THEORY OF THE ATTRACTIVE AND EXTENDED HUBBARD-MODEL IN D-DIMENSIONS

We present a variational approach for treating the Hubbard Hamiltonian in one, two and three dimensions. It is based on 2 M-fermion wavefunc tions which are allowed to form correlated spin-singlet pairs. Express ions for the ground state energy and correlation functions are derived in terms of general pair coefficient functions. The presented approac h offers a convenient starting point for improved variational treatmen ts that allow to include different specific types of pair correlations . We present first applications to the attractive and to the extended Hubbard model using a very simple ansatz for the pair coefficient func tions. The ground state energy, chemical potential, order parameter, m omentum distribution as well as spin-spin and density-density correlat ion functions follow from a system of coupled nonlinear equations that has to be solved selfconsistently. All quantities are given for arbit rary band-filling in one, two and three dimensions. Our results are co mpared with those of other approximations and for the one-dimensional case with the exact results of Krivnov and Ovchinnikov.