Spin-disordered ground state for a nearly half-filled Hubbard model

Following Nagaoka, the ground state of the large-U nearly half-filled Hubbard model is ‘‘ferromagnetic.’’ However, because of the anisotropic exchange energy ${\mathit{J}}_{\mathit{A}}$, the physical Nagaoka ground state is nondegenerate and comprises a totally disordered spin state, i.e., a linear combination of all possible spin arrangements. For this ground state the susceptibility is Pauli-like but of a magnitude associated with a narrow band of width ∼${\mathit{J}}_{\mathit{A}}$ while the holons, i.e., the charge excitations, correspond to spinless fermions with a band of width 2zt. Associated with the spinon sector are very poorly defined spin waves, i.e., bosons, with a quadratic dispersion relation. These spin waves do not become soft at any finite temperature, rather, they soften as they approach the metal-insulator transition, i.e., as the number of holes ${\mathit{n}}_0$ becomes small. Examined is the problem of constructing a mean-field slave-boson approach for the present problem.