Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2)×SU(3) Spin-Orbital Kondo Model

Hund metals have attracted attention in recent years due to their unconventional superconductivity,
which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying
Hund metals using dynamical mean-field theory, one arrives at a self-consistent “Hund impurity problem”
involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If
its spin and orbital degrees of freedom are screened at different energy scales, T sp < T orb , the intermediate
energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We
resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity
problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-of-
the-art implementation of the numerical renormalization group, capable of exploiting non-Abelian
symmetries, with a generalization of Affleck and Ludwig’s conformal field theory (CFT) approach for
multichannel Kondo models. We characterize the NFL fixed point of Hund metals in detail for a Kondo
model with an impurity forming an SUð2Þ × SUð3Þ spin-orbital multiplet, tuned such that the NFL energy
window is very wide. The impurity’s spin and orbital susceptibilities then exhibit striking power-law
behavior, which we explain using CFT arguments. We find excellent agreement between CFT predictions
and numerical renormalization group results. Our main physical conclusion is that the regime of spin-
orbital separation, where orbital degrees of freedom have been screened but spin degrees of freedom
have not, features anomalously strong local spin fluctuations: the impurity susceptibility increases as
−γ
χ imp
sp ∼ ω , with γ > 1.