Scaling theory of the Kondo screening cloud

Abstract

A scaling form for the local susceptibility, derived from renormalization group arguments, is proposed. The scale over which the uniform part of this scaling form varies can be viewed as a definition of the Kondo ``screening cloud" $\sim \xi_K$. The proposed scaling form interpolates between Ruderman-Kittel-Kasuya-Yosida (RKKY) results in the high temperature limit, $T\gg T_K$, and Fermi liquid results in the low temperature, long-distance limit, $T\ll T_K$, $r\gg \xi_K$. The predicted form of the Knight shift is longer range at low temperatures where the screening cloud has formed, than at high temperatures where it has not. Using weak and strong coupling perturbation theory combined with large scale density matrix renormalization group (DMRG) results we study the validity of the finite size version of the scaling form at $T=0$. We explicitly extract a length scale proportional to the Kondo length scale, $\xi_K$. The numerical results are in good agreement with the proposed scaling form and confirm the existence of the Kondo screening cloud.Comment: 33 pages + 12 figures in eps format. Uses Revtex3.0 and epsf.sty. RG arguments have been expande

Screening cloud in thek-channel Kondo model: Perturbative and large-kresults

“…Results on the T = 0 limit of the susceptibility scaling function were given in Ref. [ 5]. An obvious generalization of our calculations is to general frequency dependent Green's functions.…”

“…On general scaling grounds, the spatial correlators should depend on the ratio of the distance r to these two scales. Sørensen and one of us 5 have suggested a scaling form for the r-dependent Knight shift, proportional to the zero frequency spin susceptibility, which has been justified numerically and perturbatively 5,6 : χ(r, T ) − ρ/2 = cos(2k F r) 8π 2 v F r 2 f (r/ξ K , r/ξ T ).…”

“…Whether or not this large screening cloud really exists has been a controversial subject in the literature, and has recently attracted some theoretical interest [4][5][6][7][8] . Boyce and Slichter 9 had performed direct Knight shift measurements of the spin-spin correlator at all temperatures and had concluded that there was no evidence of the so-called screening cloud.…”

Cooperation of different exchange mechanisms in confined magnetic systems

“…Furthermore, it can be interpreted as a signature of the fact that each impurity is located in the exterior of the Kondo cloud of the other impurity, as the low-energy physics of the single-impurity Kondo model is essentially the one of a Fermi liquid with [13,21,22] S m s j ∼ 1/|i m − j| 2 for |i m − j| ξ K . One may explicitly derive the effective low-energy Hamiltonian by using strong-coupling degenerate perturbation theory, where hopping to and off a local Kondo singlet is treated as a weak perturbation.…”

“…It is oscillatory in the distance d of the spins, J RKKY ∼ (−1) d J 2 /d, for a non-interacting onedimensional metallic host system given by a tight-binding model with nearest-neighbor hopping t at half-filling. On the other hand, if J is much larger than t, a strongcoupling variant of RKKY exchange [12,13] can be derived perturbatively in powers of t/J. If J is antiferromagnetic, RKKY exchange typically competes with the emergence of the Kondo effect [14] which is responsible for the individual screening of impurity spins by the conduction electrons.…”