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

## TL;DR

This paper analytically and numerically investigates the non-Fermi-liquid fixed point in Hund metals, revealing the role of spin-orbital separation and providing detailed characterization using conformal field theory and numerical renormalization group methods.

## Contribution

It introduces an analytical solution for a Hund impurity model with SU(2)$\times$SU(3) symmetry, combining CFT and NRG to clarify the NFL behavior in Hund metals.

## Key findings

- Identification of a wide NFL energy window in the model.
- Power-law divergence of impurity spin susceptibility with exponent > 1.
- Excellent agreement between CFT predictions and NRG results.

## Abstract

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, $T_\mathrm{sp} < T_\mathrm{orb}$, 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 SU(2)$\times$SU(3) 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 $\chi_\mathrm{sp}^\mathrm{imp} \sim \omega^{-\gamma}$, with $\gamma > 1$.