Finite temperature dynamics of the Anderson model

TL;DR

This paper extends the local moment approach to analyze the finite-temperature dynamics and transport in the Anderson impurity model, especially in the Kondo regime, providing analytical scaling forms and good agreement with numerical results.

Contribution

The paper introduces an analytical extension of the local moment approach to finite temperatures for the Anderson model, capturing universal scaling and thermal destruction of the Kondo resonance.

Findings

Analytical scaling form for the single-particle spectrum at finite T.

Resistivity $ ho(T)$ matches NRG results at high T.

Smooth crossover to Fermi liquid behavior at low T.

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 $\omega_{\rm K}$). In particular the resultant universal scaling behaviour of the single-particle spectrum $D(\omega; T) \equiv F(\frac{\w}{\omega_{\rm K}}; \frac{T}{\omega_{\rm K}})$ 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 $D(\omega; T)$. The $T / \omega_{\rm K}$-dependence of the resulting resistivity $\rho(T)$, 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 $T/\omega_{\rm K} \sim 1$, and to cross over smoothly to the Fermi liquid form $\rho (T) - \rho (0) \propto -(T/\omega_{\rm K})^2$ in the low-temperature limit. The underlying approach, while naturally approximate, is moreover applicable to a broad range of quantum impurity and related models.