Zero-Temperature Magnetic Properties of the Hubbard Model with Infinite Coulomb Repulsion

The two-pole approximation due to Roth for electron correlation in a narrow $s$ band is applied to ferromagnetic and antiferromagnetic symmetries in simple cubic (sc) and body-centered-cubic (bcc) crystal structures and to ferromagnetic symmetry in the face-centered-cubic (fcc) structure. Numerical results in the case of zero-temperature, infinite-Coulomb-repulsion, and tight-binding nearest-neighbor band structures are presented. When the number of electrons is less than the number of sites, the paramagnetic susceptibilities of wave numbers corresponding to both magnetic symmetries exhibit two singularities as a function of electron concentration for both the sc and bcc structures, while there is no zero-wave-number singularity for the fcc structure. When the number of electrons is greater than the number of sites, there are two zero-wave-number singularities for the fcc structure and also, as a consequence of the electron-hole symmetry, there are two singularities for the sc and bcc structures. Magnetizations and energies are calculated for the various magnetic solutions as a function of electron concentration. Where it exists, the ferromagnetic solution having maximum total spin has the lowest energy. These results are in agreement with Nagaoka's conclusions for almost half-filled bands in the infinite-Coulomb-repulsion limit.