Role of non-linear susceptibilities in non-equilibrium transport through an N-level Anderson impurity model away from half-filling

We study non-equilibrium SU(N) Kondo effect that occurs in quantum impurity systems at low-temperatures T and low-bias voltages eV. We expand the differential conductance up to terms of order T² and (eV)² at arbitrary electron fillings, using an extended version of the Fermi-liquid theory for the Anderson impurity model. The coefficients for these terms are determined by the linear and non-linear susceptibilities defined with respect to the equilibrium ground state [1,2]. We calculate these susceptibilities using the NRG for N=2, 4, and 6 in a wide range of electron fillings N_d, varying the impurity level position ε_d. The results show that contributions of the three-body susceptibilities on the transport coefficients increase as N_d deviates away from half-filling, especially near the fillings of N_d = 1 and N_d = N-1. We also employ a large N approach, i.e., the 1/(N-1) expansion with a scaling that keeps (N-1)U constant [3]. We find that the 1/(N-1) results and NRG results are in good already at N=4 and 6.
[1] A. Oguri and A. C. Hewson, Phys. Rev. B 97, 035435 (2018), Erratum: B. 98. 079905 (2018).
[2] M. Filippone, C. P. Moca, A. Weichselbaum, J. von Delft, and C. Mora, Phys. Rev. B 98, 075404 (2018).
[3] A. Oguri, Phys. Rev. B 85, 155404 (2012).