Three-body Fermi liquid corrections for an infinite-$U$ SU($N$) Anderson impurity model

Abstract

We study the three-body Fermi liquid effects in the SU($N$) Anderson impurity model in the strong interaction limit where the occupation number $N_d^{}$ of the impurity levels varies over the range of $0<N_d^{}<1$. The three-body correlation of impurity electrons contributes to the next-to-leading order terms of transport coefficients at low energies when the electron-hole symmetry, the time-reversal symmetries, or both are broken by external fields or potentials. Using the numerical renormalization group approach, we calculate the differential conductance and the nonlinear current noise through quantum dots, as well as the thermal conductivity of both quantum dots and magnetic alloys. Specifically, we focus on the SU(2) and SU(4) cases and demonstrate how the three-body contributions evolve in the limit of $U\to\infty$, across the $1/N$-filling Kondo regime and the valence fluctuation regime. Our results clarify how the three-body correlation affects low-energy transport, with a crucial dependence on the occupation number $N_d^{}$. We also show that the three-body correlation strongly couples with asymmetries in the tunnel couplings between quantum dots and reservoirs; in particular it significantly affects the nonlinear current through the quarter-filling Kondo state for $N=4$.