Z3 Parafermion in the Double Charge Kondo Model

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [W. Pouse et al., Nat. Phys. (2023)] 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 Z3 parafermion emerges at the critical point, characterized by a fractional 21ln(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.