Spin Correlations and Finite-Size Effects in the One-dimensional Kondo Box

TL;DR

This paper investigates the Kondo effect in a small metallic wire using density matrix renormalization group, focusing on spin correlations, spectral density, and finite-size effects to understand the Kondo cloud and screening length.

Contribution

It provides a detailed analysis of the Kondo effect in finite systems, revealing the relationship between the Kondo resonance and the screening length, and suggests a spectroscopic method to detect the Kondo cloud.

Findings

Proportionality between Kondo resonance weight and screening length.

Finite-size effects significantly influence Kondo temperature and spectral features.

Mesoscopic variations affect the Kondo effect beyond even/odd effects.

Abstract

We analyze the Kondo effect of a magnetic impurity attached to an ultrasmall metallic wire using the density matrix renormalization group. The spatial spin correlation function and the impurity spectral density are computed for system sizes of up to L=511 sites, covering the crossover from $L<\ell_K$ to $L > \ell_K$, with $\ell_K$ the spin screening length. %Strong mesoscopic variations of the Kondo temperature $T_K$ %and of the spectral features override, to some extent, the %even/odd effect predicted earlier for averaged quantities. We establish a proportionality between the weight of the Kondo resonance and $\ell_K$ as function of $L$. This suggests a spectroscopic way of detecting the Kondo cloud.