Friedel Oscillations of Kondo Impurities: a Comparison

Recently Affleck et al. derived the existence of Friedel oscillations in the presence of a Kondo impurity. They supported their analytic derivation by numerical calculations using Wilson’s renormalization approach (NRG). In this paper the size of the Friedel oscillations is calculated with the FAIR method (Friedel Artificially Inserted Resonance) which has been recently developed. The results of NRG and FAIR are compared. The development of Friedel oscillations with a phase shift of π/2 outside of the Kondo radius is confirmed. The properties of magnetic impurities in a metal is a fascinating problem which was first studied by Friedel [1] and Anderson [2]. The disappearance of the magnetic moment at low temperatures, the Kondo effect, is one of the most intensively studied problems in solid state physics [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. In the last decade the Kondo effect has experienced a renaissance. There is a growing interest in this field [19], extending from magnetic atoms on the surface of corrals [20] to carbon nanotubes [21], quantum dots [22], [23], [24], [25], [26], [27], [28] and nanostructures [29]. There are still many open questions, particularly the real-space form of the wave function and the resulting charge density and polarization. Recently Affleck, Borda and Saleur [30] (ABS) investigated the formation of Friedel oscillations in the vicinity of a Kondo impurity. Their result has the form ρFr (r)− ρ0 = CD rD [