Overscreened multichannel Kondo model: Large solution and conformal field theory

The multichannel Kondo model with (Formula presented) spin symmetry and (Formula presented) channel symmetry is considered. The impurity spin is chosen to transform as an antisymmetric representation of (Formula presented) corresponding to a fixed number of Abrikosov fermions (Formula presented) For more than one channel (Formula presented) and all values of (Formula presented) and (Formula presented) 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-(Formula presented) limit of the model is then considered, in which (Formula presented) and (Formula presented) 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 (Formula presented) 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-(Formula presented) limit, such as the (Formula presented) 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.