Magnetic Impurity in a Metal with Correlated Conduction Electrons: An Infinite Dimensions Approach

TL;DR

This paper investigates a magnetic impurity in a correlated electron metal using an infinite-dimensional Hubbard model, revealing how electron interactions influence the Kondo temperature and the nature of the Kondo effect.

Contribution

It introduces an effective two-impurity Hamiltonian approach in infinite dimensions and analyzes the impact of electron correlations on the Kondo scale and non-Fermi-liquid behavior.

Findings

Kondo temperature decreases with increasing U.

Weak interactions enhance the Kondo scale exponentially.

Intermediate U leads to loss of exponential Kondo behavior.

Abstract

We consider the Hubbard model with a magnetic Anderson impurity coupled to a lattice site. In the case of infinite dimensions, one-particle correlations of the impurity electron are described by the effective Hamiltonian of the two-impurity system. One of the impurities interacts with a bath of free electrons and represents the Hubbard lattice, and the other is coupled to the first impurity by the bare hybridization interaction. A study of the effective two-impurity Hamiltonian in the frame of the 1/N expansion and for the case of a weak conduction-electron interaction (small U) reveals an enhancement of the usual exponential Kondo scale. However, an intermediate interaction (U/D = 1 - 3), treated by the variational principle, leads to the loss of the exponential scale. The Kondo temperature T_K of the effective two-impurity system is calculated as a function of the hybridization parameter and it is shown that T_K decreases with an increase of U. The non-Fermi-liquid character of the Kondo effect in the intermediate regime at the half filling is discussed.