Validity of Equation-of-Motion Approach to Kondo Problem in the Large-$N$ limit

TL;DR

This paper investigates the Anderson impurity model for the Kondo problem using an improved equation of motion method in the large-N limit, confirming the persistence of the Kondo resonance and its features across different N values.

Contribution

It introduces a new decoupling scheme in the EOM approach, enabling analysis of the Kondo effect for arbitrary orbit-spin degeneracy N and resolving issues present at N=2.

Findings

Kondo resonance exists for all N ≥ 2.

The approach aligns with NRG results for N=2.

Temperature affects the Kondo peak as expected.

Abstract

The Anderson impurity model for Kondo problem is investigated for arbitrary orbit-spin degeneracy $N$ of the magnetic impurity by the equation of motion method (EOM). By employing a new decoupling scheme, a set self-consistent equations for the one-particle Green function are 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 $N \geq 2$. The approach removes the pathology in the standard EOM for N=2, and has the same level of applicability as non-crossing approximation. For N=2, an exchange field splits the Kondo resonance into only two peaks, consist with the result from more rigorous numerical renormalization group (NRG) method. The temperature dependence of the Kondo resonance peak is also discussed.