Multi-impurity Anderson model for quantum dots coupled in parallel

Abstract

The system of several (N) quantum dots coupled in parallel to the same single-mode conduction channel can be modelled as a single-channel N-impurity Anderson model. Using the generalized Schrieffer-Wolff transformation we show that near the particle-hole symmetric point, the effective Hamiltonian in the local moment regime is the N-impurity S=1/2 Kondo model. The conduction-band-mediated RKKY exchange interaction between the dots is ferromagnetic and at intermediate temperatures locks the moments into a maximal spin S=N/2 ground state. We provide an analytical estimate for the RKKY interaction. At low temperatures the spin is partially screened by the conduction electrons to N/2-1/2 due to the Kondo effect. By comparing accurate numerical renormalization group results for magnetic susceptibility of the N-impuriy Anderson model to the exact Bethe-Ansatz results of a S=N/2 SU(2) Kondo system we show, that at low-temperature the quantum dots can be described by the effective S=N/2 Kondo model. Moreover, the Kondo temperature is independent of the number of impurities N. We demonstrate the robustness of the spin N/2 ground state as well as of the associated S=N/2 Kondo effect by studying the stability of the system with respect to various experimentally relevant perturbations. We finally explore various quantum phase transitions driven by these perturbations.

20 pages, 16 figures

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