Validity of the equation-of-motion approach to the Kondo problem in the large- N limit

The Anderson impurity model for Kondo problem is investigated for arbitrary spin-orbital degeneracy N of the magnetic impurity by the equation-of-motion method (EOM). By employing a different decoupling scheme, a set of self-consistent equations for the one-particle Green's function is derived and numerically solved in the large- N approximation. For the particle-hole symmetric Anderson model with finite Coulomb interaction U, we show that the Kondo resonance at the impurity site exists for all N 2. The approach removes the pathology in the standard EOM for N=2 and has the same level of applicability as noncrossing approximation. For N=2, an exchange field splits the Kondo resonance into only two peaks as predicted by a more rigorous numerical renormalization-group method. The temperature dependence of the Kondo resonance peak is also discussed.