Configuration-interaction approach to hole pairing in the two-dimensional Hubbard model

The interactions between holes in the Hubbard model, in the low density, intermediate- to strong-coupling limit, are investigated by systematically improving mean field calculations. The configuration-interaction basis set is constructed by applying to local unrestricted Hartree-Fock configurations all lattice translations and rotations. It is shown that this technique reproduces, correctly, the properties of the Heisenberg model, in the limit of large U. Upon doping, dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. The numerical results also show that when more than two holes are added to the system, they do not tend to cluster, but rather hole pairs remain far apart. Hole-hole correlations are also calculated and shown to be in qualitative agreement with exact calculations for 4 x 4 clusters. In particular our results indicate that for intermediate coupling the hole-hole correlation attains a maximum when the holes are in the same sublattice at a distance of root 2 times the lattice spacing, in agreement with exact results and the t-J model. The method is also used to derive known properties of the quasiparticle band structure of isolated spin polarons. [S0163-1829(99)15221-4].