Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency

TL;DR

This work resolves the quasi-ballistic regime of the three-channel charge Kondo model using a nonperturbative functional renormalization group approach. It reproduces the universal zero-frequency conductance at the 3CK fixed point and provides the full frequency and temperature crossovers, including a universal conductance scaling function and impurity entropy, controlled by a single scale T*. Extending the analysis to interacting leads with Luttinger parameter K, the authors uncover a continuous line of nonperturbative fixed points between ballistic and strong-coupling limits, quantified by K-dependent G* and ΔS*. The results validate FRG as a powerful tool for quantum impurity problems in regimes inaccessible to standard methods and yield quantitative predictions for mesoscopic experiments. Overall, the work bridges high-transparency and traditional Kondo regimes, establishing universal crossover physics and guiding future explorations of interacting multi-channel impurity systems.

Abstract

Quantum impurity models provide a central framework for correlated electron physics, with quantum dots enabling controlled experimental realizations. While their weak-coupling behavior is well understood through mappings to Kondo Hamiltonians, the opposite regime of highly transparent contacts has lacked a controlled theoretical description. Using the functional renormalization group (FRG), we resolve this regime for the three-channel charge Kondo device of Ref.~\cite{iftikhar2018}, benchmarking against conformal field theory by reproducing the universal zero-frequency conductance and, crucially, going beyond it to obtain the full frequency crossover of the conductance and the full temperature crossover of the impurity entropy, together with a continuous line of fixed points for interacting leads. These results establish FRG as a powerful nonperturbative tool for quantum impurity problems in regimes inaccessible to conventional approaches, with direct implications for mesoscopic experiments.

Figures (10)

• Figure 1: (Left) Experimental device from Ref. iftikhar2018: a metallic island (the Kondo impurity) with gate-induced offset charge $N_0$ is coupled to three quantum Hall edge channels via quantum point contacts. (Right) Schematic conductance $G$ as a function of energy scale $E$ (temperature or frequency) for low (blue) and high (green) transparencies. Both regimes yield the same universal zero-frequency conductance $G_{\rm 3CK}^*=2\sin^2(\pi/5)$ (red point), as predicted by conformal field theory affleck2001yi1998yi2002bao2017quantum.
• Figure 2: (Left) Universal conductance (in units of $e^2/h$) as a function of rescaled frequency $\omega/T^*$ for several $r$ values at $K=1$. The asymptotic behavior at low-frequency \ref{['eq:low_freq']} and high-frequency \ref{['eq:high_frequency_asymptotics']} is shown by (red) dashed lines, while the horizontal dash-dotted line marks the extrapolated zero-frequency limit. The red point marks the exact CFT result. Curves collapse onto a single line (the black solid line is a guide to the eye) in the wide-band limit $T^*/D\ll 1$. (Right) Universal entropy crossover at $K=1$, compared with exact thermodynamic Bethe ansatz (TBA) results.
• Figure 3: Zero-frequency conductance $G^*(K)$ as a function of $K$, along with the corresponding exponent $\nu(K)$ (right inset). Dashed lines indicate perturbative RG results near $K=3/2$, and near $K=2/3$ obtained from the dual model yi1998yi2002. The exponent $\nu$ peaks around $K=1$ (right inset). The left inset shows the residual impurity entropy $\Delta S^*(K)$. Solid (black) lines are guides to the eye.
• Figure 4: Universal conductance scaling function $\mathcal{G}$ for several $K$ values. Markers correspond to $r/D \in \{0.005, 0.01, 0.05\}$. Lines are guides to the eye.
• Figure S1: Equivalent classical circuit describing the experimental setup of Ref. sm_iftikhar2018. Each QPC is defined by its own resistance.