Spin susceptibility of Anderson impurities in arbitrary conduction bands

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