1/Nexpansion 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)${\pi }^2$=5${\pi }^2$/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 χ/γ ratio: We may write (S/T${\chi }_0$)=[2${\pi }_B^{22}$/$g^2$(j+1)${\mu }_B^2$](1-1/N)(π/N) cot(π/N), which is a universal result in the Kondo regime.