Fermi-liquid theory for the single-impurity Anderson model

Christophe Mora, Catalin Pascu Moca, Jan von Delft, Gergely Zarand

Published 2014-09-11Version 1

We generalize Nozi\`eres' Fermi-liquid theory for the low-energy behavior of the Kondo model to that of the single-impurity Anderson model. In addition to the electrons' phase shift at the Fermi energy, the low-energy Fermi-liquid theory is characterized by four Fermi-liquid parameters, which we express in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives w.r.t. the local level position. We determine these in terms of the bare parameters of the Anderson model using Bethe Ansatz and Numerical Renormalization Group (NRG) calculations. Our low-energy Fermi-liquid theory applies throughout the crossover from the strong-coupling Kondo regime via the mixed-valence regime to the empty-orbital regime. From the Fermi-liquid theory, we determine the conductance through a quantum dot symmetrically coupled to two leads in the regime of small magnetic field, low temperature and small bias voltage, and compute the coefficients of the $\sim B^2$, $\sim T^2$, and $\sim V^2$ terms. The coefficients of $T^2$ and $V^2$ are found to change sign during the Kondo to empty-orbital crossover, while that of $\sim B^2$ remains positive. The crossover becomes universal in the limit that the local interaction is much larger than the level width.