High-energy dynamics of the single-impurity Anderson model

Abstract

The quantitative control of the dynamic correlations of single impurity Anderson models is essential in several very active fields. We analyze the one-particle Green function with a constant energy resolution by dynamic density-matrix renormalization. In contrast to other approaches, sharp dominant resonances at high energies are found. Their origin and importance are discussed.PACS numbers: 71.55. Ak, 71.28.+d, 71.27.+a, and 78.67.Hc Single impurity models are at the very basis of the description of strong correlation phenomena. Landmarks are the Kondo problem 1 and the single impurity Anderson model (SIAM) 2 , for a review see Ref.3. The interest in the quantitative analysis of SIAMs has been intensified considerably by the advent of a systematic mapping of strongly correlated lattice models to effective SIAMs supplemented by a self-consistency condition. This is the key point of dynamic mean-field theory (DMFT) 4,5 which is based on an appropriate scaling of the non-local parts of the Hamiltonian 6,7 , for reviews see Ref. 8,9. In recent years, the DMFT is applied very successfully in combination with ab-initio density functional calculations 10,11 . In this way, the unbiased knowledge about the bands could be enhanced by the inclusion of interaction effects between the excited quasi-particles. It turned out that the combination of density functional results and DMFT makes the quantitative understanding of spectroscopic data possible 12 . So far, the methods applied to the SIAM were designed to capture the low-energy physics, in particular the fixed points and the thermodynamics 13,14 . The numerical renormalization group (NRG) was later extended to calculate also dynamic, i.e., spectral information. It provides reliable data on the scale of the Kondo temperatures T K , see Ref. 3,15 and references therein. On larger scales, the energy resolution is less well-controlled.But in various applications the behavior at higher energies is important to achieve quantitative accuracy. For instance, the self-consistency cycle of the DMFT mixes modes at all energies. Hence, excellent quantitative control over the dynamics at high energies is indispensable, even if finally only the behavior at low energies matters.Another application is the optical control of isolated S = 1/2 impurities or quantum dots coupled to narrow bands. If the impurities differ so that the energy between the singly occupied ground state and the excited double occupancy differs, they can be switched selectively from the ground state to the double occupancy (and back) by shining light at the resonant frequency onto the sample. The life-time of the double occupancy, i.e., the inverse line width of the resonance, determines how well the resonance condition has to be met, how selective the switching can be, and how stable the excited state is.In view of the above, we perform a numerical investigation which aims to describe both the low-energy dynamics and the high-energy dynamics quantitatively. To this end, we use an energy resolution which is con...

Spectral functions and time evolution from the Chebyshev recursion

“…We compare our results with the dynamic DMRG results from Ref. [16], which are believed to be highly reliable. In particular, we compare computations in the formerly suggested setup [13,17] that uses the Chebyshev recursion for b = 0 in Eq.…”

“…As an example, we compute the spectral function of the single impurity Anderson model (SIAM), which serves as a common benchmark [13,14,16,22,23] and is highly relevant as it is at the core of dynamical mean-field theory (DMFT) [24][25][26][27].…”

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

“…The direct inversion of the resolvent operator can be carried out with a procedure such as the conjugate gradient method, but this procedure is computationally costly and can be unstable. (These problems can be minimized by a better choice of methods for the inversion [153].) A variant of this method was introduced by Jeckelmann [154] which leads to a more efficient and stable method.…”

“…2.4.2 and was further developed and successfully applied in Ref. [153]. In this approach, the target vectors…”

Dynamical Mean-Field Approximation and Cluster Methods for Correlated Electron Systems

“…At T = 0, there exists presently not yet a reliable tool to solve quantum impurity models with substantially more that two impurity degrees of freedom (spin degeneracy). First attempts to use the density matrix renormalization group method to solve quantum impurity problems can for example be found in [31,32,33].…”