APPROXIMATIONS TO THE 2-HOLE GROUND-STATE OF THE HUBBARD-ANDERSON MODEL - A NUMERICAL TEST

Several resonating-valence-bond-type states are being considered as an approximation of the two-hole ground state of the two-dimensional Hub bard-Anderson model. These states have been carefully constructed by T raa and Gaspers with such algebraic properties, as to optimise differe nt contributions of the Hubbard-Anderson hamiltonian. In this paper, t he different contributions to their energies are calculated for lattic es with sizes from 8 x 8 up to 16 x 16 and periodic boundary condition s, using a variational Monte-Carlo method. We show which state is lowe st in energy and, more important, why this is so. In accordance with t he optimal state from this tested set, we propose a bound state. It wi ll be shown that this state is indeed the most stable state.