Scaling theory of the Kondo screening cloud

TL;DR

This paper proposes a scaling form for the Kondo screening cloud's spatial extent, connecting high and low temperature behaviors, and confirms its validity through analytical and numerical methods.

Contribution

It introduces a new scaling form for the Kondo screening cloud that unifies different temperature regimes and validates it with DMRG simulations.

Findings

The scaling form interpolates between RKKY and Fermi liquid results.

Numerical results confirm the existence of the Kondo screening cloud.

A length scale proportional to the Kondo length is explicitly extracted.

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.