Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling

We extend the microscopic Fermi-liquid theory for the Anderson impurity to explore non-equilibrium transport at finite magnetic fields. Using the Ward identities with the analytic and anti-symmetric properties of the vertex function, the Fermi-liquid corrections of order T² and (eV)² are determined at low temperatures T and low bias voltages eV [1]. The results can be compared with those obtained recently in the Nozières phenomenological description [2]. Away from half-filling, these corrections can be expressed in terms of the linear and non-linear static susceptibilities which represent the two-body flucutuations (2BF) and three-body fluctuations (3BF), respectively. We calculate these coefficients for the conductance through a quantum dot using the numerical renormalization group. At zero magnetic field, the 2BF dominate the corrections in the Kondo regime. The 3BF become significant far away from half-filling, especially in the valence-fluctuation regime and empty-orbital regimes. In contrast, at finite magnetic fields, the contributions of the 3BF become comparable to those of the 2BF.

[1] A. Oguri and A. C. Hewson, arXiv:1709.06385; arXiv:1710.02948; arXiv:1710.04575.
[2] M. Filippone, C. Moca, J. von Delft, and C. Mora, Phys. Rev. B 95, 165404 (2017).