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arXiv:2509.03612 · Physical Review Letters

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

Nicolas Paris, N. Dupuis, Christophe Mora

Published Jan 26, 2026• 3 citations
arXivHTMLPDF

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 Iftikhar et al. [Tunable quantum criticality and super-ballistic transport in a "charge" Kondo circuit, Science 360, 1315 (2018)SCIEAS0036-807510.1126/science.aan5592], 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.

DOI
10.1103/7h3l-5k99

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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 Iftikhar et al. [Tunable quantum criticality and super-ballistic transport in a "charge" Kondo circuit, Science 360, 1315 (2018)SCIEAS0036-807510.1126/science.aan5592], 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.
Quantum phase transitions (QPTs) are ubiquitous in strongly correlated materials. However, the microscopic complexity of these systems impedes the quantitative understanding of QPTs. We observed and thoroughly analyzed the rich strongly correlated physics in two profoundly dissimilar regimes of quantum criticality. With a circuit implementing a quantum simulator for the three-channel Kondo model, we reveal the universal scalings toward different low-temperature fixed points and along the multiple crossovers from quantum criticality. An unanticipated violation of the maximum conductance for ballistic free electrons is uncovered. The present charge pseudospin implementation of a Kondo impurity opens access to a broad variety of strongly correlated phenomena.
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We theoretically investigate the thermoelectric transport through a circuit implementation of the three-channel charge Kondo model quantum simulator [Z. Iftikhar et al., Science 360, 1315 (2018)SCIEAS0036-807510.1126/science.aan5592]. The universal temperature scaling law of the Seebeck coefficient is computed perturbatively approaching the non-Fermi liquid strong coupling fixed point using the Abelian bosonization technique. The predicted T^{1/3}logT scaling behavior of the thermoelectric power sheds light on the properties of Z_{3} emerging parafermions and gives access to exploring prefractionalized zero modes in the quantum transport experiments. We discuss a generalization of approach for investigating a multichannel Kondo problem with emergent Z_{N}→Z_{M} crossovers between "weak" non-Fermi liquid regimes corresponding to different low-temperature fixed points.
We study a charge two-channel Kondo model, demonstrating that recent experiments [Z. Iftikhar et al, Nature (London) 526, 233 (2015)] realize an essentially perfect quantum simulation-not just of its universal physics, but also nonuniversal effects away from the scaling limit. Numerical renormalization group (RG) calculations yield conductance line shapes encoding RG flow to a critical point involving a free Majorana fermion. By mimicking the experimental protocol, the experimental curve is reproduced quantitatively over 9 orders of magnitude, although we show that far greater bandwidth/temperature separation is required to obtain the universal result. Fermi liquid instabilities are also studied: In particular, our exact analytic results for nonlinear conductance provide predictions away from thermal equilibrium, in the regime of existing experiments.
This thesis explores several fundamental topics in mesoscopic circuitry that incorporates few electronic conduction channels. The first experiments address the quantized character (the discreteness) of charge in circuits. We demonstrate the charge quantization criterion, observe the predicted charge quantization scaling and demonstrate a crossover toward a universal behavior as temperature is increased. The second set of experiments addresses the unconventional quantum critical physics that arises in the multichannel Kondo model. By implementing a Kondo impurity with a pseudo-spin of ½ constituted by two degenerate charge states of a circuit, we explore the two- and three-channel Kondo physics. At the symmetric quantum critical point, we observe the predicted universal Kondo fixed points, scaling exponents and validate the full numerical renormalization group scaling curves. Away from the quantum critical point, we explore the crossover from quantum criticality: direct visualization of the development of a quantum phase transition, the parameter space for quantum criticality, as well as universality and scaling behaviors.
We study triangular clusters of three spin-1/2 Kondo or Anderson impurities that are coupled to two conduction leads. In the case of Kondo impurities, the model takes the form of an antiferromagnetic Heisenberg ring with Kondo-type exchange coupling to continuum electrons. We show that this model exhibits many types of the behavior found in various simpler one- and two-impurity models, thereby enabling the study of crossovers between a number of Fermi-liquid (FL) and non-Fermi-liquid (NFL) fixed points. In particular, we explore a direct crossover between the two-impurity Kondo-model NFL fixed point and the two-channel Kondo-model NFL fixed point. We show that the concept of the two-stage Kondo effect applies even in the case when the first-stage Kondo state is of NFL type. In the case of Anderson impurities, we consider the transport properties of three coupled quantum dots. This class of models includes, as limiting cases, the familiar serial double quantum dot and triple quantum dot nanostructures. By extracting the quasiparticle scattering phase shifts, we compute the low-temperature conductance as a function of the interimpurity tunneling coupling. We point out that due to the existence of exponentially low-temperature scales, there is a parameter range where the stable ``zero-temperature'' fixed point is essentially never reached (not even in numerical renormalization group calculations). The zero-temperature conductance is then of no interest and it may only be meaningful to compute the conductance at finite temperature. This illustrates the perils of studying the conductance in the ground state and considering thermal fluctuations only as a small correction.