We report numerical results for the two-dimensional Hubbard model in the strong-coupling approximation, including the three-site terms omitted in the t-J model, for a 4×4 system with periodic boundary conditions. We study the one- and two-hole band structures, the root-mean-square hole-hole separation, and the hole-hole binding energy for both the t-J and the strong-coupling models. In the physical parameter region (8<U/t<40) believed appropriate for the high-temperature superconductors, the three-site terms enhance the hole mobility, increasing the one- and two-hole bandwidths and decreasing the binding energy, but changing the hole-hole separation only slightly; quantitative differences between the models range up to 40%. The transition (at large U/t) to the ferromagnetic Nagaoka state is sharper in the strong-coupling model; our results do not support a transition through all intermediate S values in the bulk.

• Received 10 July 1992

DOI:https://doi.org/10.1103/PhysRevB.47.6004