Numerical study of the Kondo cloud using finite-U slave bosons

Abstract

In this work, using the finite-U slave boson mean-field approximation to solve the single-impurity Anderson model, the authors apply two different strategies to study the Kondo cloud, by analyzing quantities that are dependent on the distance to the magnetic impurity and then finding a universal distance scale ${\ensuremath{\xi}}_{K}$ through the collapse of the results into an universal function. The first method is based on the analysis of the local density of states of the conduction electrons (denoted as ${\ensuremath{\xi}}_{K}^{L})$, while the second relies on the analysis of spin correlations $({\ensuremath{\xi}}_{K}^{\mathrm{\ensuremath{\Sigma}}})$. Our calculations show that there is exact quantitative agreement, in the way ${\ensuremath{\xi}}_{K}$ depends on $U/\mathrm{\ensuremath{\Gamma}}$, between ${\ensuremath{\xi}}_{K}^{\mathrm{\ensuremath{\Sigma}}}$ and the results obtained through the heuristic expression ${\ensuremath{\xi}}_{K}\ensuremath{\propto}{v}_{F}/{T}_{K}$, while there is very close quantitative agreement between ${\ensuremath{\xi}}_{K}^{\mathrm{\ensuremath{\Sigma}}}$ and ${\ensuremath{\xi}}_{K}^{L}$. The use of the slave boson technique to calculate the spin correlations, which eliminates finite size effects, allowed us to study very large Kondo clouds, something that is very difficult using other techniques, like the density matrix renormalization Group method, for example. In addition, the very smooth curves obtained for the spin correlations allowed us to qualitatively identify a region in the Kondo cloud, adjacent to the impurity, that had been connected to the free orbital fixed point in previous numerical renormalization group calculations [Phys. Rev. B 84, 115120 (2011)].