Quantum Critical Point between Two-Channel Kondo and Fermi-Liquid Phases

TL;DR

This paper explores quantum critical points between two-channel Kondo and Fermi-liquid phases in multi-orbital impurity models, revealing a universal residual entropy of log(phi) at the transition, using numerical renormalization group analysis.

Contribution

It demonstrates the emergence of a universal residual entropy log(phi) at quantum critical points between two-channel Kondo and Fermi-liquid phases in multi-orbital systems.

Findings

Residual entropy of log(phi) observed at critical points.

Quantum critical point appears between two-channel Kondo and Fermi-liquid phases.

Universal behavior across different ions and crystal field configurations.

Abstract

We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an $f$-electron entropy of a seven-orbital impurity Anderson model hybridized with three ($\Gamma_7$ and $\Gamma_8$) conduction bands with the use of a numerical renormalization group method First we consider the case of Pr$^{3+}$ ion, in which quadrupole two-channel Kondo effect is known to occur for the local $\Gamma_3$ doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from $\Gamma_3$ doublet to $\Gamma_1$ singlet or $\Gamma_5$ triplet, we commonly observe a residual entropy of $\log \phi$ with the golden ratio $\phi=(1+\sqrt{5})/2$, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd$^{3+}$ ion, in which magnetic two-channel Kondo phase is found to occur for the local $\Gamma_6$ doublet state. We envisage a scenario that the quantum critical point characterized by $\log \phi$ generally appears between two-channel Kondo and Fermi-liquid phases.