Fermi-liquid corrections to non-equilibrium Keldysh vertex functions for an Anderson impurity model.

We study in detail the residual interaction between quasi-particles that plays an essential role in the non-equilibrium transport through quantum dots under finite bias voltage eV. Specifically, Fermi-liquid corrections to the vertex functions, which can be related to the collision integral for the Anderson impurity model, are calculated away from half-filling up to linear terms with respect to ω, ω', and eV at zero temperature T=0. Here, ω and ω' correspond to the energies of two interacting quasi-particles. The expansion coefficients are obtained by extending the recent developments [1,2], using the Ward-Takahashi identity for the Keldysh current vertex functions. We also discuss low-energy behavior of nonlinear current noise in the Fermi-liquid regime using the numerical renormalization group appraoch.
[1] A. Oguri and A. C. Hewson, PRL 120, 126802 (2018); PRB 97, 043508 (2018); PRB 97, 035435 (2018); PRB 98, 079905(E)(2018).
[2] M. Filippone, C. Moca, A.\Weichselbaum, J. von Delft, and C. Mora, PRB 98, 075404 (2018); C. Mora, C. Moca, J. von Delft, and G. Zaránd, PRB 92, 075120 (2015).