  Recently it was shown that the multipolar Kondo problem, wherein a quantum
impurity carrying higher-rank multipolar moments interacts with conduction
electrons, leads to novel non-Fermi liquid states. Because of the multipolar
character of the local moments, the form of the interaction with conduction
electrons is strongly dependent on the orbital-symmetry of the conduction
electrons via crystalline symmetry constraints. This suggests that there may
exist a variety of different non-Fermi liquid states in generic multipolar
Kondo problems depending on the character of conduction electrons. In this
work, using renormalization group analysis, we investigate a model where the
multipolar local moment is coupled to conduction electrons with two different
orbital-symmetry components, namely $p$-wave and $f$-wave symmetries. When each
orbital-symmetry component is present alone, non-Fermi liquid states with
exactly the same thermodynamic singularities appear. When both orbital-symmetry
components are allowed, however, a completely different non-Fermi liquid state
arises via the quantum fluctuations in the mixed scattering channels. This
remarkable result suggests that the multipolar Kondo problem presents novel
opportunities for the discovery of unexpected non-Fermi liquid states.
