| We present an analysis of the Friedel oscillations surrounding a quantum impurity, confirming previous theoretical work establishing the existence of a length-scale connected to the Kondo temperature RK ∼ 1/TK. Furthermore, we show that the underlying RG structure of such problems is fully apparent in real-space quantities, with the Kondo length-scale simply being a particular case. More generally, RG flow between any pair of fixed points results in a characteristic energy scale; and a corresponding length-scale appears. In particular, the popular screening cloud scenario for the Anderson model is refined: a moment only forms on length-scales ∼ RLM (corresponding to RG flow from free orbital to local moment fixed points), which is then screened on distances ∼ RK (corresponding to RG flow to the strong coupling fixed point). These notions are generalized in the study of the softgap Anderson model (realized by an impurity in graphene), where the vanishing Kondo temperature at the quantum phase transition shows up as a diverging length-scale. |
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