We propose a theoretical model to detect the quantum phase transition in a triangular quantum dot molecule with frustration. The boundaries of the phase diagram are accurately determined by the transmission. For small frustration t, as the interdot Coulomb repulsion V increases, the system undergoes a Kosterlitz–Thouless（KT） transition from the Kondo resonance state with a transmission peak at zero energy to the Coulomb blocked state with zero transmission, which is followed by a first transition to the V-induced resonance（VIR） state with unitary transmission. For large frustration t, as V increases, the orbital spin singlet without transmission transits to the VIR state through a KT transition.
We study the charge oscillation in the triangular quantum dots symmetrically coupled to the leads. A strong charge oscillation is observed even for a very small level difference. We attribute this oscillation behaviour to the many- body effect in the strongly correlated system instead of the physical scenarios based on the mean-field approach in the previous works for the two-level dot. The level difference induces the difference of the occupations between different dots, while the symmetry of the many-body states favours the homogeneous distribution of the charge density on the three dots. The interplay of these two factors results in the charge oscillation.
