Three-channel charge Kondo model at high transparency

Abstract: Quantum impurity models involving a localized charge that is weakly coupled to electronic leads usually map to Kondo-like Hamiltonians that exhibit various quantum critical behaviors. Here, we address the opposite regime of high contact transparency by solving the model of a quantum island coupled to three quantum Hall edge channels. Using a functional renormalization group (FRG) approach, we demonstrate that the low-energy physics is controlled by a nonperturbative fixed point. The universal energy crossover in both the linear conductance and the impurity entropy is obtained. We reproduce the zero-frequency conductance and the leading low-energy exponent of the three-channel Kondo model, confirming their universality across all transparencies. For interacting leads -- a model that continuously connects to the pseudo-gap Kondo model at low transparency -- we find a line of fixed points as the Luttinger parameter $K$, which encodes the strength of the interactions, changes. Our work demonstrates that FRG methods are an efficient tool for solving quantum impurity problems in regimes where standard approaches fail.