Low-energy physics of three-orbital impurity model with Kanamori interaction

TL;DR

This paper analyzes the low-energy behavior of a three-orbital Anderson impurity model with Kanamori interaction, revealing slow spin screening and emergent SU(3) orbital symmetry through perturbative and numerical methods.

Contribution

It demonstrates that the three-orbital model exhibits emergent SU(3) symmetry and slow spin screening, connecting it to related impurity problems and providing detailed renormalization group analysis.

Findings

Orbital couplings dominate over spin couplings in the Kondo regime.

SU(3) orbital symmetry is dynamically established at low energies.

Spin and orbital Kondo temperatures depend on interaction parameters and hybridization.

Abstract

We discuss the low-energy physics of the three-orbital Anderson impurity model with the Coulomb interaction term of the Kanamori form which has orbital SO(3) and spin SU(2) symmetry and describes systems with partially occupied $t_{2g}$ shells. We focus on the case with two electrons in the impurity that is relevant to Hund's metals. Using the Schrieffer-Wolff transformation we derive an effective Kondo model with couplings between the bulk and impurity electrons expressed in terms of spin, orbital, and orbital quadrupole operators. The bare spin-spin Kondo interaction is much smaller than the orbit-orbit and spin-orbital couplings or is even ferromagnetic. Furthermore, the perturbative scaling equations indicate faster renormalization of the couplings related to orbital degrees of freedom compared to spin degrees of freedom. Both mechanisms lead to a slow screening of the local spin moment. The model thus behaves similarly to the related quantum impurity problem with a larger SU(3) orbital symmetry (Dworin-Narath interaction) where this was first observed. We find that the two problems actually describe the same low-energy physics since the SU(3) symmetry is dynamically established through the renormalization of the splittings of coupling constants to zero. The perturbative renormalization group results are corroborated with the numerical-renormalization group (NRG) calculations. The dependence of spin Kondo temperatures and orbital Kondo temperatures as a function of interaction parameters, the hybridization, and the impurity occupancy is calculated and discussed.