Fermi-liquid theory for the single-impurity Anderson model

Abstract

We generalize Nozières' 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: the two given by Nozières that enter to first order in the excitation energy, and two additional ones that enter to second order and are needed away from particle-hole symmetry. We express all four parameters in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives with respect to 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 \textit{exactly} in terms of the Fermi-liquid parameters. The coefficients of $T^2$, $V^2$ and $B^2$ are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.

17 pages, 10 figures

References in corpus (14)

• Kondo effect in quantum dots
• Full counting statistics for the Kondo dot in the unitary limit
• Mesoscopic to universal crossover of transmission phase of multi-level quantum dots
• Shot noise near the unitary limit of a Kondo quantum dot
• Current noise through a Kondo quantum dot in a SU(N) Fermi liquid state
• Shot Noise in SU(N) Quantum Dot Kondo Effects
• Fermi liquid theory for SU(N) Kondo model
• The Kondo crossover in shot noise of a single quantum dot with orbital degeneracy
• Conductance scaling in Kondo correlated quantum dots: role of level asymmetry and charging energy
• Universal scaling in nonequilibrium transport through an Anderson impurity
• Field dependent quasiparticles in a strongly correlated local system II
• Renormalized perturbation theory and scaling for an impurity Anderson model
• Equilibrium Fermi-liquid coefficients for the fully screened N-channel Kondo model
• Transport properties of fully screened Kondo models

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