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Antiferro-quadrupole state of orbital-degenerate Kondo lattice model with f^2 configuration

To clarify a key role of $f$ orbitals in the emergence of antiferro-quadrupole structure in PrPb$_{3}$, we investigate the ground-state property of an orbital-degenerate Kondo lattice model by numerical diagonalization techniques. In PrPb$_{3}$, Pr$^{3+}$ has a $4f^{2}$ configuration and the crystalline-electric-field ground state is a non-Kramers doublet $Γ_{3}$. In a $j$-$j$ coupling scheme, the $Γ_{3}$ state is described by two local singlets, each of which consists of two $f$ electrons with one in $Γ_{7}$ and another in $Γ_{8}$ orbitals. Since in a cubic structure, $Γ_{7}$ has localized nature, while $Γ_{8}$ orbitals are rather itinerant, we propose the orbital-degenerate Kondo lattice model for an effective Hamiltonian of PrPb$_{3}$. We show that an antiferro-orbital state is favored by the so-called double-exchange mechanism which is characteristic of multi-orbital systems.