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

Abstract

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 $U_{\mathrm{eff}}$ as the $k=0\mathrm{}$ reversed-spin self-energy for $U\to \infty$, divided by the number $n\uparrow$ of up-spin electrons per site, we find that the present result departs rather rapidly from the Kanamori result as $n\uparrow$ is increased, and it is concluded that the Kanamori result overestimates the increase in $U_{\mathrm{eff}}$ with $n\uparrow$, at least in the present case. For intermediate values of $n\uparrow$, the two-pole approximation of the previous article and the present calculation give very similar results for this quantity.