The two-hole ground state of the Hubbard-Anderson model, approximated by a variational RVB-type wave function

In this paper the Hubbard-Anderson model on a square lattice with two holes is studied. The ground state (GS) is approximated by a variational RVB-type wave function. The holes interact by exchange of a localized spin excitation (SE), which is created or absorbed if a hole moves to a nearest-neighbour site. An SE can move over the sublattice on which it is created. A variational calculation of the GS and the GS-energy is performed for an open-ended 4 × 4 lattice with two holes with the restriction that the SE is neighbouring both holes and does not move over its sublattice. It is found that the two holes prefer a bound state in which their mutual distance is 1 or 2 (with lattice spacing 1).