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

作者：Laura M. Roth · 发表于：Physical Review · 年份：1969 · DOI：10.1103/physrev.186.428 · 被引用次数：59 · 研究领域：Physics of Superconductivity and Magnetism、Advanced Chemical Physics Studies、Quantum and electron transport phenomena

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