Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory

Details Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory

1997-11-19

arxiv.org/abs/cond-mat/9711192v2

Physics

Condensed Matter

Strongly Correlated Electrons

39 pages, RevTeX, including 5 figures in encapsulated postscript format

Scientific paper

10.1103/PhysRevB.58.3794

The multichannel Kondo model with SU(N) spin symmetry and SU(K) channel symmetry is considered. The impurity spin is chosen to transform as an antisymmetric representation of SU(N), corresponding to a fixed number of Abrikosov fermions $\sum_{\alpha}f_{\alpha}^{\dagger}f_{\alpha}=Q$. For more than one channel (K>1), and all values of N and Q, the model displays non-Fermi behaviour 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 and Q/N 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 $\omega/T$, also predicted from 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 ``non-crossing approximation'' and the previous work of Cox and Ruckenstein are discussed.

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