On the solution of the Coqblin-Schreiffer Hamiltonian by the large-N expansion technique

Abstract

The authors employ a functional integral approach to the Coqblin-Schreiffer Hamiltonian, similar to that of Yoshimori and Sakurai (YS-1970) for the Kondo Hamiltonian, except that a field lambda enforcing the constraint nf=1 is introduced. By a gauge transformation they show that the phase of the complex sigma field introduced by YS may be absorbed into lambda , leading to a new two-field formulation in terms of lambda and s= mod sigma mod . The static approximation leads to a simple Friedel resonance on the impurity of width approximately TK/N, where N=2J+1 is the number of channels, and whose position is determined by the Friedel sum rule, as in the 'local Fermi liquid' theory. The authors show that the charge susceptibility is zero, is required. Gaussian fluctuation corrections to the static approximation are determined' taking account of fermion propagator renormalisation they then find that the Wilson chi / gamma ratio R=N/(N-1) is correct to order 1/N2. The value of TK is that of a lowest-order renormalisation group treatment, but may be corrected by fluctuation effects.