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arXiv:cond-mat/9508030

Is there an exponentially large Kondo screening cloud ?

Erik Schwartz Sørensen, Ian K. Affleck

Published Aug 9, 1995• 0 citations
arXivHTMLPDF

Abstract

We make a precise scaling conjecture, based on renormalization group ideas, regarding the screening cloud around an impurity spin in the Kondo effect and test it numerically using the Density Matrix Renormalization Group method.
DOI
10.48550/arxiv.cond-mat/9508030

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A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms---the gate potential and a magnetic field---which destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.
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A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms -- the gate potential and a magnetic field -- that destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.
We analyze the ground-state energy, magnetization, magnetic susceptibility, and Kondo screening cloud of the symmetric single-impurity Anderson model (SIAM) that is characterized by the bandwidth WWW, the impurity interaction strength UUU, and the local hybridization VVV. We compare Gutzwiller variational and magnetic Hartree-Fock results in the thermodynamic limit with numerically exact data from the density-matrix renormalization group (DMRG) method on large rings. To improve the DMRG performance, we use a canonical transformation to map the SIAM onto a chain with half the system size and open boundary conditions. We compare to Bethe ansatz results for the ground-state energy, magnetization, and spin susceptibility that become exact in the wide-band limit. Our detailed comparison shows that the field-theoretical description is applicable to the SIAM on a ring for a broad parameter range. Hartree-Fock theory gives an excellent ground-state energy and local moment for intermediate and strong interactions. However, it lacks spin fluctuations and thus cannot screen the impurity spin. The Gutzwiller variational energy bound becomes very poor for large interactions because it does not describe properly the charge fluctuations. Nevertheless, the Gutzwiller approach provides a qualitatively correct description of the zero-field susceptibility and the Kondo screening cloud. The DMRG provides excellent data for the ground-state energy and the magnetization for finite external fields. At strong interactions, finite-size effects make it extremely difficult to recover the exponentially large zero-field susceptibility and the mesoscopically large Kondo screening cloud.