Spin susceptibility of Anderson impurities in arbitrary conduction bands

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 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 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 loc and to compare them with chi imp obtained by the traditional NRG. Our results indicate that those exotic behaviors observed in chi 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 loc less accurate than chi imp, the FDM method allows a high-precision dynamical calculation of chi loc at much reduced computational cost, with an accuracy at least one order higher than chi imp. Moreover, artifacts in the FDM algorithm to chi 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.