Dynamic susceptibilities of the single-impurity Anderson model within an enhanced noncrossing approximation

Abstract

The single-impurity Anderson model is studied within an enhanced noncrossing approximation (ENCA). This method is extended to the calculation of susceptibilities and thoroughly tested, also in order to prepare applications as a building block for the calculation of susceptibilities and phase transitions in correlated lattice systems. A wide range of model parameters, such as impurity occupancy, temperature, local Coulomb repulsion, and hybridization strength, are studied. Results for the spin and charge susceptibilities are presented. By comparing the static quantities to exact Bethe ansatz results, it is shown that the description of the magnetic excitations of the impurity within the ENCA is excellent, even in situations with large valence fluctuations or vanishing Coulomb repulsion. The description of the charge susceptibility is quite accurate in situations where the singly occupied ionic configuration is the unperturbed ground state; however, it seems to overestimate charge fluctuations in the asymmetric model at too low temperatures. The dynamic spin-excitation spectrum is dominated by the Kondo screening of the impurity spin through the conduction band, i.e., the formation of the local Kondo singlet. A finite local Coulomb interaction $U$ leads to a drastic reduction in the charge response as processes involving the doubly occupied impurity state are suppressed. In the asymmetric model, the charge susceptibility is enhanced for excitation energies smaller than the Kondo scale ${T}_{K}$ due to the influence of valence fluctuations.