Quantum Phase Transitions And Many-body Effects In Strongly Correlated Triple Quantum Dots Systems

In this thesis, we use numerical renormalization group (NRG) method to investi-gate the quantum phase transitions and many-body effect in a strongly correlated triple quantum dots system. By analysing the local spin, the charge on the dots and their correlation functions, we got the ground-state phase diagram and the charge oscillation of the models at zero temperature.We first study the quantum phase transition (QPT) and electronic transport in triple quantum dots for a wide range of the charge energy c. We focus on the effect of the interdot repulsion V and the magnetic field B. In the case of particle-hole (p-h) sym-metry and B=0, we find the local quadruplet-doublet transition of first order when V increases to a critical point Vc≈U, where U is the on-site repulsion. Beyond the p-h symmetry, the sequence of the QPTs depends on∈. For small∈, a first order dou-blet-singlet transition is observed. For middle∈, we find the quadruplet-triplet tran-sition of first order at Vc1and the triplet-singlet transition of the Kosterlitz-Thouless type at Vc2. For large∈, there are two kinds of first order QPT with phase sequence quadruplet-triplet-doublet. The magnetic field B compensates for the effect of V. For V> U, as B increases we find a first order or second order QPT from a low-spin state to a high-spin state. The restoring of the Kondo effect and a perfect spin filtering is realized in the appropriate regime of the magnetic field.Then we study the charge oscillation in the parallel triple quantum dots symmetri-cally coupled to the leads. A strong charge oscillation is observed even for very small level difference. We attribute this oscillation behavior to the many-body effect in the strongly correlated system, instead of the physical scenarios based on the mean-field approach in previous works for two-level dot. The level difference induces the differ-ence of the occupations between different dots while the symmetry of many-body states favors the homogeneous distribution of the charge density on three dots. The interplay of these two factors results in the charge oscillation.