We introduce an improved approach for obtaining smooth finite-temperature spectral functions of quantum impurity models using the numerical renormalization group (NRG) technique. It is based on calculating first the Green's function on the imaginary-frequency axis, followed by an analytic continuation to the real-frequency axis using Padé approximants. The arbitrariness in choosing a suitable kernel in the conventional broadening approach is thereby removed and, furthermore, we find that the Padé method is able to resolve fine details in spectral functions with less artifacts on the scale of ω ∼ T . We discuss the convergence properties with respect to the NRG calculation parameters (discretization, truncation cutoff) and the number of Matsubara points taken into account in the analytic continuation. We test the technique on the the single-impurity Anderson model and the Hubbard model (within the dynamical mean-field theory). For the Anderson impurity model, we discuss the shape of the Kondo resonance and its temperature dependence. For the Hubbard model, we discuss the inner structure of the Hubbard bands in metallic and insulating solutions at half-filling, as well as in the doped Mott insulator. Based on these test cases we conclude that the Padé approximant approach provides more reliable results for spectral functions at low-frequency scales of ω T and that it is capable of resolving sharp spectral features also at high frequencies. It outperforms broadening in most respects.

No abstract

We study the antiferromagnetic phase of the Kondo lattice model on bipartite lattices at half-filling using the dynamical mean-field theory with numerical renormalization group as the impurity solver, focusing on the detailed structure of the spectral function, self-energy, and optical conductivity. We discuss the deviations from the simple hybridization picture, which adequately describes the overall band structure of the system (four quasiparticle branches in the reduced Brillouin zone), but neglects all effects of the inelastic-scattering processes. These lead to additional structure inside the bands, in particular asymmetric resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic Kondo insulator quantum phase transition. These features, which we name "spin resonances", appear generically in all models where the f -orbital electrons are itinerant (large Fermi surface) and there is Néel antiferromagnetic order (staggered magnetization), such as periodic Anderson model and Kondo lattice model with antiferromagneitc Kondo coupling, but are absent in antiferromagnetic phases with localized f -orbital electrons (small Fermi surface), such as the Kondo lattice model with ferromagnetic Kondo coupling. We show that with increasing temperature and external magnetic-field the spin resonances become suppressed at the same time as the staggered magnetization is reduced. Optical conductivity σ(Ω) has a threshold associated with the indirect gap, followed by a plateau of low conductivity and the main peak associated with the direct gap, while the spin resonances are reflected as a secondary peak or a hump close to the main optical peak. This work demonstrates the utility of high-spectralresolution impurity solvers to study the dynamical properties of strongly correlated fermion systems.

We study the antiferromagnetic and the paramagnetic Kondo insulator phases of the Kondo lattice model on the cubic lattice at half-filling using the cellular dynamical mean-field theory (CDMFT) with numerical renormalization group (NRG) as the impurity solver, focusing on the fine details of the spectral function and self-energy. We find that the non-local correlations increase the gap in both the antiferromagnetic and the Kondo insulator phase and shrink the extent of the antiferromagnetic phase in the phase diagram but do not alter any properties qualitatively. The agreement between the numerical CDMFT results and those within a simple hybridization picture, which adequately describes the overall band structure of the system but neglects all effects on the inelastic-scattering processes, is similar to that of the single-site DMFT results; there are deviations that are responsible for the additional fine structure, in particular for the asymmetric spectral resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic quantum phase transition. These features appear broader in the CDMFT mostly due to numerical artifacts linked to more aggressive state truncation required in the NRG.