Transport coefficients of the Anderson model via the numerical renormalization group

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Abstract
The transport coefficients of the Anderson model are calculated by extending Wilson's numerical renormalization group method to finite-temperature Green functions. Accurate results for the frequency and temperature dependence of the single-particle spectral densities and transport time tau ( omega , T) are obtained and used to extract the temperature dependence of the transport coefficients in the strong-correlation limit of the Anderson model. Results are obtained for values of the local level position ranging from the Kondo regime to the mixed valency and empty orbital regimes. The low-temperature anomalies in the resistivity, rho (T), thermopower, S(T), thermal conductivity, kappa (T), and Hall coefficient, RH(T), are discussed in terms of the behaviour of the spectral densities. At low temperature all quantities exhibit the expected Fermi liquid behaviour, rho (T)= rho 0(1-c(T/TK)2), S(T) approximately gamma T, kappa (T)/ alpha T=1+ beta (T/TK)2, RH(T)=-Rinfinity (1- delta (T/TK)2). Analytic results based on Fermi liquid theory are derived here for the first time for beta and the numerical results are shown to be consistent with this coefficient. The range of temperatures over which universal behaviour extends is also discussed. Scattering of conduction electrons in higher-angular-momentum, l>0, channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of the interference terms between the resonant l=0 and non-resonant l=1 channels on the transport properties. The presence of non-resonant scattering is shown to be particularly important for the thermopower at half filling, where the sign of the thermopower can depend sensitively on the non-resonant phase shift. Finally the relation of the results to experiment is discussed.
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