$\mathbb{Z}_3$ parafermion in the double charge-Kondo model

TL;DR

This paper demonstrates that a double charge-Kondo model can host a $$3 parafermion at its critical point, characterized by fractional residual entropy and charge, supported by analytical and numerical methods aligning with experimental observations.

Contribution

It reveals the emergence of $$3 parafermions in a double charge-Kondo model using bosonization, Bethe-ansatz, and numerical renormalization group analysis, connecting theory with experiments.

Findings

Identification of $$3 parafermion at the critical point.

Observation of fractional residual entropy $rac{1}{2} ext{ln}(3)$.

Conductance behavior consistent with experimental data.

Abstract

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a $\mathbb{Z}_3$ parafermion emerges at the critical point, characterized by a fractional $\tfrac{1}{2}\ln(3)$ residual entropy, and scattering fractional charges $e/3$. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.