ESR in a gapped Anderson model

We applied the numerical renormalization group method to study the electron spin resonance (ESR) of a single-impurity Anderson model with a gap Δ in the conduction electron density of states, centered at the Fermi level. We analyzed the relaxation rate 1 / T 1 of a magnetic probe located at a position R → around the Anderson impurity. It presents different behaviors for the symmetric and the asymmetric case. For the symmetric case and any Δ > 0 , 1 / T 1 goes to a constant for T ≪ Γ k (Kondo resonance). 1 / T 1 decreases monotonically to zero only for Δ = 0 . For the asymmetric case, there is a Δ under which 1 / T 1 decreases monotonically to zero as T → 0 , and above which 1 / T 1 saturates, as occurs in the symmetric case for Δ > 0 . This behavior indicates a quantum phase transition from the quenched to the unquenched magnetic moment in the ground state of the Anderson ion.