Dynamics of the Anderson Model for Dilute Magnetic Alloys: A Quantum Monte Carlo and Maximum Entropy Study

Abstract

The single-impurity Anderson model1 was invented nearly thirty years ago to describe dilute magnetic impurities in metallic hosts, including the formation and properties of itinerant local moments in alloys. The model is a prerequisite for the understanding of mixed valent and heavy-fermion phenomena.2 A limit of the model is the famous Kondo model3 which describes resistivity minima and saturation. The model is simple to state and its properties are readily measureable in the laboratory.4 However, the solution of the model is a difficult many-body problem. In recent years considerable progress in understanding the static properties of the model has been achieved using non-perturbative methods such as the Bethe ansatz,5 the renormalization group,6 and quantum Monte Carlo (QMC).7 Nevertheless, the understanding of the dynamical properties has remained elusive. These include the spectral density of the impurity state, the transport coeffecients, and the dynamical magnetic susceptibility. The spectral density has been calculated reliably only for large orbital degeneracy8 or for expansion parameters below the range of most physical interest.9 It has been obtained only at zero temperature by the renormalization group method,10 and it is extremely difficult to calculate reliably from QMC.11-15