Three Types of Non-Fermi-Liquid Fixed Point for a Triplet Quantum Impurity in a Cubic Metal

Abstract

In cubic metals, a local, magnetic moment with a triplet ground state coupled to $\Gamma_8$ conduction electrons can give rise to various non-Fermi liquid (NFL) quantum critical behaviors. To date, only those exchange couplings have been studied that are spherically symmetric already in the high-temperature, local moment regime. Namely, only the effects of potential scattering, dipolar spin exchange, i.e. Kondo, and quadrupolar exchange couplings were considered, and two types of NFL fixed points have been identified. However, in cubic symmetry, six independent exchange couplings can be present in the Hamiltonian: in addition to the spherically symmetric potential scattering and Kondo exchange, there are four independent, spherical-symmetry-breaking Hamiltonian terms: two quadrupolar-quadrupolar, a dipolar-octupolar and a quadrupolar-octupolar exchange interaction, where the first/second element of the compound adjectives refers to the impurity/conduction-electron transitions. While all of them flow to fixed points where rotational invariance is recovered, I found that one of the quadrupolar-quadrupolar couplings flows to a previously unidentified NFL fixed point. I derive the exchange couplings allowed by cubic symmetry, solve them with the numerical renormalization group, and present three types of NFL excitation spectrum$-$one of which is novel, at least in the context of a quantum impurity with a triplet ground state.