Spectral properties of the two-impurity Anderson model with varying distance and various interactions

Abstract

We present an approximation for the treatment of two interacting magnetic impurities immersed into a noninteracting metallic host. The scheme is based on direct perturbation theory with respect to the hybridization between the impurity and band electrons. This two-impurity enhanced noncrossing approximation can fully incorporate the indirect interactions between the impurities that are mediated by the conduction electrons as well as additional arbitrary direct interaction matrix elements. We qualify the approximation by investigating the uncoupled case and conclude that the two-impurity approximation is equally accurate as its single-impurity counterpart. The physical properties of the two-impurity Anderson model are first investigated in some limiting cases. In a regime where each of the uncoupled two impurities would exhibit a pronounced Kondo effect, we ignore the indirect coupling via the conduction band and only incorporate direct interactions. For a ferromagnetic direct exchange coupling, the system displays a behavior similar to a spin-one Kondo effect, while an antiferromagnetic coupling competes with the Kondo effect and produces a pseudogap in the many-body Kondo resonance of the single-particle spectral function. Interestingly, a direct one-particle hopping also produces a pseudogap, but additionally pronounced side peaks emerge. This gap is characteristically different from the case with antiferromagnetic coupling since it emerges as a consequence of distinct Kondo effects for the bonding and antibonding orbital, i.e., it reflects a splitting of even and odd parity states. For the general case of only indirect coupling via the conduction band, the results show signatures of all the previously discussed limiting cases as a function of the impurity-impurity distance. Oscillatory behavior in physical quantities is to be expected due to the generated Ruderman-Kittel-Kasuya-Yosida interaction. We are led to the conclusion that the well-known Doniach scenario captures essential aspects of this model, but the details, especially at small distances, are more complicated.

Interplay between the Kondo effect and the Ruderman–Kittel–Kasuya–Yosida interaction

“…3c, where the spectra are normalized to their value at the Fermi energy. Similar results were obtained recently by applying perturbation theory 38 .…”

Fine structure of the spectra of the Kondo lattice model: Two-site cellular dynamical mean-field theory study

“…37. Using larger supercells is probably prohibitive in the NRG, but one could use the non-local DMFT to study several two-site clusters and merge the correlations 38 . We show how to construct the coefficients for a generic impurity Hamiltonian without any symmetries:…”

Effective low-energy description of the two-impurity Anderson model: RKKY interaction and quantum criticality

“…4 proves the restoring of the P-H symmetry around the Fermi energy by adding the additional counter term. In the absence of the counter term, the spectral function (black line) is asymmetric and the Kondo peak is split [23,47,68] as can be seen in the inset of Fig. 4.…”

“…The transition between these two singlet phases in the TIAM is driven by the ratio between the Kondo temperatur T K and J RKKY [40,[44][45][46][47][48][49][50]. While a quantum critical point (QCP) separates both ground states in the presence of a special kind of particle-hole (P-H) symmetry [22,43,49], the quantum phase transition is replaced by a crossover if that symmetry is broken [51].…”