Thermoelectric transport and current noise through a multilevel Anderson impurity: Three-body Fermi-liquid corrections in quantum dots and magnetic alloys

We present a comprehensive Fermi-liquid description of thermoelectric transport and shot noise, applicable to multilevel quantum dots (QDs) and magnetic alloys (MAs) without electron-hole or time-reversal symmetry [1,2]. Our formulation is based on a series of Ward identities for an Anderson model with N discrete impurity levels and is asymptotically exact at low but finite temperatures (T) or finite bias voltages (eV), up to next-to-leading order terms. These next-to-leading order terms of transport coefficients are shown to be fully described by a set of Fermi-liquid parameters, including three-body nonlinear susceptibilities, in addition to the linear ones and the occupation number N_d of impurity electrons, defined with respect to the equilibrium ground state. We apply this formulation to SU(N) symmetric QDs and MAs for N=4 and 6, exploring the role of three-body correlations across the entire range of impurity-electron fillings 0 < N_d < N. This includes the SU(N) Kondo regimes at various integer-filling points, as well as the valence fluctuation regimes, using the numerical renormalization group approach. [1] Y. Teratani, K. Tsutsumi, K. Mototyama, R. Sakano, and A. Oguri, PRB 110, 035308 (2024). [2] A. Oguri, Y. Teratani, K. Tsutsumi, R. Sakano, PRB 105, 115409 (2022).