<i>1/N</i>expansion for the transport coefficients of the single-impurity Anderson model

Abstract

In this paper the properties of the single-impurity Anderson model are studied via a loop expansion using the functional-integral method developed by Read and Newns, referred to here as I. First, the low-temperature equilibrium properties were considered and it was shown that, to two-loop order after zero modes are properly treated, for physical properties (free energy and f-level occupancy) the loop expansion is one-to-one with the 1/N expansion and to order 1/N the results first derived by Read, referred to here as II, were recovered. For the transport properties we present the first calculations of the low-temperature conductivity, thermopower, and thermal conductivity to order 1/N. For the conductivity, our result for the ${T}^{2}$ coefficient in the Kondo limit when N=6 is (1-8/3N)${\ensuremath{\pi}}^{2}$=5${\ensuremath{\pi}}^{2}$/9=5.6 which is to be compared with the result 5, derived previously from the ``noncrossing'' approximation. In the case of the thermal power S, our result agreed to order 1/N with the exact result derived here for the first time. In the Kondo regime, this implies that the thermopower is reduced by a factor of (1-1/N) relative to the mean-field result, and that this is an exact ratio, analogous to the well-known \ensuremath{\chi}/\ensuremath{\gamma} ratio: We may write (S/T${\ensuremath{\chi}}_{0}$)=[2${\ensuremath{\pi}}_{B}^{22}$/${g}^{2}$(j+1)${\ensuremath{\mu}}_{B}^{2}$](1-1/N)(\ensuremath{\pi}/N) cot(\ensuremath{\pi}/N), which is a universal result in the Kondo regime.