Transport Coefficients of the Anderson Model via the Numerical Renormalization Group

TL;DR

This paper extends the Numerical Renormalization Group method to finite temperatures to accurately compute transport properties of the Anderson model, revealing Fermi liquid behavior and effects of non-resonant scattering.

Contribution

It introduces a finite-temperature NRG approach for transport coefficients in the Anderson model, including higher angular momentum channels and non-resonant scattering effects.

Findings

Transport coefficients follow Fermi liquid power laws at low T.

Accurate spectral densities and transport times obtained.

Non-resonant scattering influences transport properties.

Abstract

The transport coefficients of the Anderson model are calculated by extending Wilson's NRG method to finite temperature Green's 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. The low temperature anomalies in the resistivity, $\rho(T)$, thermopower, $S(T)$, thermal conductivity $\kappa(T)$ and Hall coefficient, $R_{H}(T)$, are discussed. All quantities exhibit the expected Fermi liquid behaviour at low temperature with power law dependecies on $T/T_{K}$ in very good agreement with analytic results based on Fermi liquid theory. Scattering of conduction electrons in higher, $l>0$, angular momentum channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of non--resonant scattering on the transport properties.