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arXiv:2411.10778 · Physical review. B./Physical review. B

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

Kaiji Motoyama, Yoshimichi Teratani, Kazuhiko Tsutsumi, Kohei Wake, Ryosuke Kobayashi, Rui Sakano, Akira Oguri

Published Jun 4, 2025• 1 citation
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Abstract

We study the three-body Fermi liquid effects in the SU($N$) Anderson impurity model within the strong interaction limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$, where the occupation number ${N}_{d}^{}$ of the impurity levels varies over the range of $0<{N}_{d}^{}<1$. The three-body correlations arise among the impurity electrons when the electron-hole symmetry, the time-reversal symmetry, or both are broken by external fields or potentials. They play a key role in low-energy transport, particularly in the next-to-leading-order terms of power expansion with respect to temperature $T$ and bias voltage $eV$. Using the numerical renormalization group approach, we calculate the differential conductance and 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, demonstrating how the three-body correlations evolve in the strong interaction limit across the $1/N$-filling Kondo regime at ${N}_{d}^{}\ensuremath{\simeq}1.0$ and the valence fluctuation regime where the occupation number ${N}_{d}^{}$ varies rapidly with the position ${\ensuremath{\epsilon}}_{d}^{}$ of the impurity levels. We also show that the three-body correlations strongly couple with asymmetries in the tunnel couplings between quantum dots and reservoirs. For $N=4$, this coupling significantly affects the order ${(eV)}^{3}$ nonlinear current through the quarter-filling Kondo state, where the electron-hole symmetry is broken. In particular, in the $U\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, the expansion coefficients exhibit clear plateau structures associated with the Kondo effect at ${N}_{d}^{}\ensuremath{\simeq}1.0$. Our formulation and analysis pave the way for deducing the three-body correlations from the low-energy experiments on the next-to-leading-order transport.

DOI
10.1103/physrevb.111.235301

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