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

Abstract

The single impurity Anderson model (SIAM) is studied within an enhanced non-crossing 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 of 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 TK due to the influence of valence fluctuations.

Kinks in the electronic dispersion of the Hubbard model away from half filling

“…Generally, the agreement between the three methods is very good and deviations only occur at large energies, establishing the too low energy scale to be the main source of discrepancy between the ENCA and RG methods. The deviations for ω/T * 1 observable in panel (b) are on the one hand due to the improper description of correlated valence fluctuations 17,52 and on the other hand due to the thermal broadening required in ENCA.…”

“…While magnetic properties, i.e., the magnetic susceptibility, are described excellently, charge fluctuations are not as well accounted for. 52 In the spectral functions, where spin and charge fluctuations contribute equally, this leads to an overestimation of the height of the many-body resonance at the Fermi level at too low temperatures. The dynamic charge susceptibility is overestimated for very low frequencies.…”

“…53,54 The ENCA removes the cusps associated with this pathology 20 and significantly improves the Fermi liquid properties of the spectral functions and dynamic susceptibilities. 17,52 However, the skeleton diagrams selected within the ENCA still suffer from an imbalance between charge and spin excitations. While magnetic properties, i.e., the magnetic susceptibility, are described excellently, charge fluctuations are not as well accounted for.…”

Accuracy of density functionals for molecular electronics: The Anderson junction

“…A central object in the Anderson junction is the charge susceptibility, χ c ( n C ) = d n C /dµ. At half-filling, this is known analytically [33,34]:…”

Extension of dynamical mean-field theory by inclusion of nonlocal two-site correlations with variable distance

“…36 Too low temperatures can not be investigated with our impurity solver due to the violation of Fermi liquid properties. 28,37 Additionally, in the high-energy part of the spectrum the inclusion of additional neighbors seems to bring out more of the van-Hove singularities at ω = ±D of the original unperturbed (U = 0) spectrum [see inset of Fig. 2(a)].…”