Overscreened multichannelSU(N)Kondo model: Large-Nsolution and conformal field theory

Abstract

The multichannel Kondo model with $\mathrm{SU}(N)$ spin symmetry and $\mathrm{SU}(K)$ channel symmetry is considered. The impurity spin is chosen to transform as an antisymmetric representation of $\mathrm{SU}(N),$ corresponding to a fixed number of Abrikosov fermions ${\ensuremath{\sum}}_{\ensuremath{\alpha}}{f}_{\ensuremath{\alpha}}^{\ifmmode\dagger\else\textdagger\fi{}}{f}_{\ensuremath{\alpha}}=Q.$ For more than one channel $(K>1),$ and all values of $N$ and $Q,$ the model displays non-Fermi behavior associated with the overscreening of the impurity spin. Universal low-temperature thermodynamic and transport properties of this non-Fermi-liquid state are computed using conformal field theory methods. A large-$N$ limit of the model is then considered, in which $K/N\ensuremath{\equiv}\ensuremath{\gamma}$ and $Q/N\ensuremath{\equiv}{q}_{0}$ are held fixed. Spectral densities satisfy coupled integral equations in this limit, corresponding to a (time-dependent) saddle point. A low-frequency, low-temperature analysis of these equations reveals universal scaling properties in the variable $\ensuremath{\omega}/T,$ in agreement with conformal invariance. The universal scaling form is obtained analytically and used to compute the low-temperature universal properties of the model in the large-$N$ limit, such as the $T=0$ residual entropy and residual resistivity, and the critical exponents associated with the specific heat and susceptibility. The connections with the ``noncrossing approximation'' and the previous work of Cox and Ruckenstein are discussed.