Finite temperature dynamics of the Anderson model

Abstract

The recently introduced local moment approach (LMA) is extended to encompass single-particle dynamics and transport properties of the Anderson impurity model at finite-temperature, T. While applicable to arbitrary interaction strengths, primary emphasis is given to the strongly correlated Kondo regime (characterized by the T=0 Kondo scale $ω_{\rm K}$). In particular the resultant universal scaling behaviour of the single-particle spectrum $D(ω; T) \equiv F(\frac{\w}{ω_{\rm K}}; \frac{T}{ω_{\rm K}})$ within the LMA is obtained in closed form; leading to an analytical description of the thermal destruction of the Kondo resonance on all energy scales. Transport properties follow directly from a knowledge of $D(ω; T)$. The $T / ω_{\rm K}$-dependence of the resulting resistivity $ρ(T)$, which is found to agree rather well with numerical renormalization group calculations, is shown to be asymptotically exact at high temperatures; to concur well with the Hamann approximation for the s-d model down to $T/ω_{\rm K} \sim 1$, and to cross over smoothly to the Fermi liquid form $ρ(T) - ρ(0) \propto -(T/ω_{\rm K})^2$ in the low-temperature limit. The underlying approach, while naturally approximate, is moreover applicable to a broad range of quantum impurity and related models.