Anderson Impurity Model & Kondo Resonance

A magnetic impurity in a metal hosts a local level ε_d. When U (Coulomb repulsion) is large, a spin-1/2 moment forms. At low temperatures T < T_K, the Kondo effect screens this moment via spin-flip scattering, creating a sharp resonance in the local density of states exactly at the Fermi level (ω=0).

Anderson Parameters

T_K = —
Local DOS A(ω) = Im[G^ret(ω)]/(-π). Hartree-Fock self-energy gives lower/upper Hubbard peaks at ε_d and ε_d+U. Kondo resonance (Abrikosov-Suhl) has width ~T_K = D·exp(πε_d(ε_d+U)/(2ΓU)), pinned at ω=0 by Friedel sum rule.