Spectral properties and quantum phase transitions in parallel triple quantum dots

The spectral properties and the quantum phase transitions in parallel triple quantum dot systems are investigated using the numerical renormalization-group method. For small interdot hopping t, the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between the dots is identified in the spectra and is consistent with that obtained by the perturbation theory. With increasing t, due to the competition between the RKKY exchange and the direct exchange between dots, there exist two first-order quantum phase transitions between the phases with the local spin S-dot=3/2, 1/2, and 0 on the dots. At low temperature, the local spin S-dot=3/2 is partially screened to a residual spin S=1, while the local spin S-dot=1/2 is totally screened. In both local quadruplet and doublet states, the Kondo resonance accompanied with a conductance of the unitary limit 2e(2)/h is observed, while no Kondo effect is found in the local spin-singlet state.