Spin susceptibility of Anderson impurities in arbitrary conduction bands

TL;DR

This paper uses the full density-matrix NRG to accurately compute the local spin susceptibility of Anderson impurities in arbitrary conduction bands, clarifying previous unphysical results and establishing a reliable method for such calculations.

Contribution

The work introduces a high-precision, efficient FDM NRG method for calculating impurity spin susceptibility in arbitrary bands, correcting unphysical behaviors from traditional NRG.

Findings

Exotic behaviors in previous susceptibility calculations are unphysical.

Impurity in arbitrary bands remains a Fermi liquid and paramagnetic.

FDM NRG provides more accurate and computationally efficient susceptibility calculations.

Abstract

Spin susceptibility of Anderson impurities is a key quantity in understanding the physics of Kondo screening. Traditional numerical renormalization group (NRG) calculation of the impurity contribution $\chi_{\textrm{imp}}$ to susceptibility, defined originally by Wilson in a flat wide band, has been generalized before to structured conduction bands. The results brought about non-Fermi-liquid and diamagnetic Kondo behaviors in $\chi_{\textrm{imp}}$, even when the bands are not gapped at the Fermi energy. Here, we use the full density-matrix (FDM) NRG to present high-quality data for the local susceptibility $\chi_{\textrm{loc}}$ and to compare them with $\chi_{\textrm{imp}}$ obtained by the traditional NRG. Our results indicate that those exotic behaviors observed in $\chi_{\textrm{imp}}$ are unphysical. Instead, the low-energy excitations of the impurity in arbitrary bands only without gap at the Fermi energy are still a Fermi liquid and paramagnetic. We also demonstrate that unlike the traditional NRG yielding $\chi_{\textrm{loc}}$ less accurate than $\chi_{\textrm{imp}}$, the FDM method allows a high-precision dynamical calculation of $\chi_{\textrm{loc}}$ at much reduced computational cost, with an accuracy at least one order higher than $\chi_{\textrm{imp}}$. Moreover, artifacts in the FDM algorithm to $\chi_{\textrm{imp}}$, and origins of the spurious non-Fermi-liquid and diamagnetic features are clarified. Our work provides an efficient high-precision algorithm to calculate the spin susceptibility of impurity for arbitrary structured bands, while negating the applicability of Wilson's definition to such cases.