Abstract
In order to comprehend the mechanism of high-temperature superconductors, a strongly correlated electronic system is studied numerically in this thesis. We use a variational approach with exactly strong-correlated constraint to gain insight into the physical properties of t-t'-t''-J model. Various variational trial wave functions have been utilized to obtain the results compared with different kinds of experiments. In the hole-doped systems, we examine the evolution of ground states described by different variational wave functions and properties of the quasihole and -particle excitations of the d-wave resonating-valence-bond superconducting state. Properties related to the Fermi surface geometry deduced from quasi-hole energy dispersion of the superconducting state is shown to be consistent with the observation by photoemission spectroscopy. Comparisons of various physical observable quantities between theories and experiments in cuprates show an overall qualitative agreement on their doping dependence. With the calculated spectral weights for adding and removing an electron, we show that the product of weights is equal to the pairing amplitude squared. In addition, we derive a rigorous relation of spectral weight with doping in the electron-doped system and obtain particle-hole asymmetry of the conductance-proportional quantity within the superconducting gap. In the electron-doped systems, we present several zero-temperature phase diagrams for proper bare parameters t0 and t00. Compared with the recent results obtained by angle-resolved photoemission spectroscopy (ARPES), we show that based on the long-range-ordered antiferromagnetic metallic state prohibiting vacant sites, our results lead to qualitatively similar trends in ARPES spectra and Fermi surface topology. Additionally, the results about the evolution of the energy gap and spectral weight as a function of doping will be discussed.