Electron Correlation in Narrow Energy Bands. II. One Reversed Spin in an Otherwise Fully Aligned Narrow S Band

In a previous paper, a new Green's-function decoupling scheme was applied to the Hubbard Hamiltonian, and an improved version of Hubbard's first approximation was obtained. That result did not reduce to the correct low-density limit as obtained by Kanamori. In the present article, the theory is improved for the special case of a single reversed spin in an otherwise fully aligned band, and the improved theory is correct in the low-density limit. Numerical results are presented for the simple cubic lattice. If we define an effective exchange-interaction parameter Ueff as the $k=0$ reversed-spin self-energy for U→∞, divided by the number n↑ of up-spin electrons per site, we find that the present result departs rather rapidly from the Kanamori result as n↑ is increased, and it is concluded that the Kanamori result overestimates the increase in Ueff with n↑, at least in the present case. For intermediate values of n↑, the two-pole approximation of the previous article and the present calculation give very similar results for this quantity.