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A multichannel Kondo model, where two or more equivalent but independentchannels of electrons compete to screen a spin-1/2 impurity, showsovercompensation of the impurity spin, leading to the non-Fermi-liquid behaviorin various thermodynamic and transport properties. However, when the channelsymmetry is broken, an impurity quantum phase transition can occur at zerotemperature. Identification of an order parameter describing the impurityquantum phase transition is very difficult since it is beyond the conventionalLandau-Ginzburg-Wilson theory. By employing the natural orbitalsrenormalization group method, we study both two-channel and threechannel Kondomodels, from the perspective of spin correlation between the impurity andelectrons in electronic channels. Here we demonstrate that by introducing thespin-correlation ratio as an order parameter we can characterize impurityquantum phase transitions driven by channel asymmetry. In particular, theuniversal critical exponents $\beta$ of the spin-correlation ratio and $\nu$ ofthe correlation length are explicitly determined by finite-sizescalinganalysis, namely, $\beta = 0.10(1), \nu = 2.0(1)$, and $\beta = 0.10(1), \nu =2.5(1)$ for the two-channel and three-channel Kondo models, respectively.

Order parameter for the multichannel Kondo model at quantum criticality