When the ground state of a localized ion is a non-Kramers doublet, such localized ions may carry multipolar moments. For example, Pr${}^{3+}$ ions in a cubic environment would possess quadrupolar and octupolar, but no magnetic dipole, moments. When such multipolar moments are placed in a metallic host, unusual interactions between these local moments and conduction electrons arise, in contrast to the familiar magnetic dipole interactions in the classic Kondo problem. In this work, we consider the interaction between a single quadrupolar-octupolar local moment and conduction electrons with $p$-orbital symmetry as a concrete model for the multipolar Kondo problem. We show that this model can be written most naturally in the spin-orbital entangled basis of conduction electrons. Using this basis, the perturbative renormalization group (RG) fixed points are readily identified. There are two kinds of fixed points, one for the two-channel Kondo and the other for a novel fixed point. We investigate the nature of the novel fixed point non-perturbatively using non-abelian bosonization, current algebra and conformal field theory approaches. It is shown that the novel fixed point leads to a, previously unidentified, non-Fermi liquid state with entangled spin and orbital degrees of freedom, which shows resistivity $\rho \sim T^{\Delta }$ and diverging specific heat coefficient $C/T\sim T^{-1+2\Delta }$ with $\Delta =1/5$. Our results open up the possibility of myriads of non-Fermi liquid states, depending on the choices of multipolar moments and conduction electron orbitals, which would be relevant for many rare-earth metallic systems.

中文翻译：

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多极近藤问题中非费米液体不动点的批判理论

当局部离子的基态是非克拉默斯双峰时，这种局部离子可能会携带多极矩。例如Pr${}^{3+}$立方环境中的离子将具有四极和八极，但没有磁偶极矩。当将这种多极矩放置在金属主体中时，与经典近藤问题中常见的磁偶极子相互作用相反，这些局部矩与传导电子之间会出现异常相互作用。在这项工作中，我们考虑了单个四极八极局部矩与传导电子之间的相互作用。$p$轨道对称性作为多极近藤问题的具体模型。我们表明，该模型可以最自然地在传导电子的自旋轨道纠缠基础上编写。在此基础上，可以容易地确定摄动重归一化组（RG）的不动点。有两种固定点，一种用于两通道近藤，另一种用于新颖的固定点。我们使用非阿贝尔玻色化，当前代数和共形场理论方法非扰动地研究新型定点的性质。结果表明，新颖的不定点导致了一种先前未知的非费米液态，具有自旋和轨道自由度纠缠，表明电阻率$\rho 〜{Ť}^{\Delta }$ 和发散比热系数 $C/Ť〜{Ť}^{-\mathrm{1个}+2\Delta }$ 与 $\Delta =\mathrm{1个}/5$。我们的研究结果揭示了无数非费米液态的可能性，这取决于多极矩和传导电子轨道的选择，这与许多稀土金属系统有关。