Multipole correlations in low-dimensional f-electron systems

TL;DR

This study uses density matrix renormalization group methods to explore ground-state properties and multipole correlations in a one-dimensional three-orbital Hubbard model, revealing orbital ordering and magnetic states influenced by crystalline electric field effects.

Contribution

It provides new insights into multipole correlations and orbital ordering in low-dimensional f-electron systems under varying crystal field conditions.

Findings

Orbital ordering pattern is sensitive to cubic crystalline electric field parameter B_4^0.

At B_4^0=0, a ferro-orbital state and antiferromagnetic state are observed.

Crucial role of multipole correlations in determining ground-state properties.

Abstract

By using a density matrix renormalization group method, we investigate the ground-state properties of a one-dimensional three-orbital Hubbard model on the basis of a j-j coupling scheme. For $B_4^0 \ne 0$, where $B_4^0$ is a parameter to control cubic crystalline electric field effect, one orbital is itinerant, while other two are localized. Due to the competition between itinerant and localized natures, we obtain orbital ordering pattern which is sensitive to $B_4^0$, leading to a characteristic change of $\Gamma_{3g}$ quadrupole state into an incommensurate structure. At $B_4^0 = 0$, all the three orbitals are degenerate, but we observe a peak at $q = 0$ in $\Gamma_{3g}$ quadrupole correlation, indicating a ferro-orbital state, and the peak at $q = \pi$ in $\Gamma_{4u}$ dipole correlation, suggesting an antiferromagnetic state. We also discuss the effect of $\Gamma_{4u}$ octupole on magnetic anisotropy.