Multipole Correlations in Low-Dimensionalf-Electron Systems

By using a density matrix renormalization group method, we investigate theground-state properties of a one-dimensional three-orbital Hubbard model on thebasis of a j-j coupling scheme. For $B_4^0 \ne 0$, where $B_4^0$ is a parameterto control cubic crystalline electric field effect, one orbital is itinerant,while other two are localized. Due to the competition between itinerant andlocalized natures, we obtain orbital ordering pattern which is sensitive to$B_4^0$, leading to a characteristic change of $\Gamma_{3g}$ quadrupole stateinto an incommensurate structure. At $B_4^0 = 0$, all the three orbitals aredegenerate, but we observe a peak at $q = 0$ in $\Gamma_{3g}$ quadrupolecorrelation, indicating a ferro-orbital state, and the peak at $q = \pi$ in$\Gamma_{4u}$ dipole correlation, suggesting an antiferromagnetic state. Wealso discuss the effect of $\Gamma_{4u}$ octupole on magnetic anisotropy.Comment: 4 pages, 3 figures, Proceedings of ASR-WYP-2005 (September 27-29, 2005, Tokai