Hubbard model with one hole: Ground-state properties

The ground state of the two-dimensional Hubbard model on a square lattice is studied in the large-U limit in a half-filled band with a dynamical hole. For a 4×4 lattice with hopping t=1 and coupling J<$J_c$≊0.075, the ground state has zero momentum (k) and spin 15/2 (ferromagnetic background). For J≥$J_c$ the ground state is degenerate with nonzero k and spin 1/2, in agreement with recent variational calculations. The nonzero k of the ground state comes from a nontrivial phase in the overlap of the spin states before and after a hole move. For small lattices we show that the effective Hamiltonian of the hole is that of a particle moving in a magnetic field. We also find that many of the features of the weak-coupling region carry over continuously to the strong-coupling region.