Relevance of Anisotropy in the Kondo Effect: Lessons From the Symplectic Case

TL;DR

This paper investigates the stability of the exotic non-Fermi liquid fixed point in a symplectic Kondo model, revealing that anisotropy and asymmetries destabilize it, contrary to previous beliefs, with implications for experimental realizations.

Contribution

It clarifies the stability conditions of the symplectic Kondo fixed point, showing how anisotropy and asymmetry affect its stability and identifying relevant operators.

Findings

Asymmetry destabilizes the non-Fermi liquid fixed point.

Perturbations generate the same relevant operators.

Relevance of anisotropy depends on the group generators' span.

Abstract

A Kondo model with symplectic symmetry was recently put forward as the effective low-energy theory of a superconducting-island device coupled to multiple leads. This model, which possesses non-Fermi liquid physics and effective anyons, was argued to belong to the class of topological Kondo effects. Here, we clarify the extent of stability of its exotic fixed point using perturbative and numerical renormalization group in conjunction with bosonization and conformal field theory. In contrast to previous claims, we show that asymmetry in the coupling to the leads destabilizes the non-Fermi liquid. Other destabilizing perturbations include asymmetry in the superconducting pairing or internal energy of the individual quantum dots in the island. Nevertheless, these perturbations all generate the same relevant operators. Thus, only a small number of couplings need to be tuned individually, and these can be selected according to experimental convenience. Our results highlight a common misconception that anisotropy in single-channel Kondo couplings is always irrelevant. As demonstrated, relevant terms will emerge whenever the group generators do not span the full space of impurity operators. This calls for a more detailed inspection of models that exhibit this property, such as large-spin impurities and SO(M) Kondo models.