在這篇論文裡，我們主要以數值方式來研究強相關電子系統，進一步來了解高溫超導體內的機制。
我們利用變分蒙地卡羅法來準確應付強相關系統的限制，深刻的理解在廣義t-t'-t''-J模型下的許多物理性質。
各種不同變分波函數也被拿來計算得到許多與實驗滿意的結果。

　在電洞摻雜的系統裡，我們檢視了各種不同基態隨著摻雜的演化以及d波超導態的準洞與準粒子激發態的特性。
我們也發現從超導態的準洞能量色散得到的費米面特性相當的吻合光電子能譜的實驗結果。數個實驗與理論物理量的
比較顯示出整體摻雜依賴在定性上的符合。而且我們證明了加減一個電子的能譜權值的乘積恰好等於超導序參量的平方。
除此之外，我們更得到在電子摻雜系統中能譜權值的嚴格數學等式，微分電導的電子電洞反對稱性，
以及電子的強相關聯與配對的關聯性。

　至於電子摻雜的系統，我們首先呈現了許多不同t'與t''裸參數所對應的零溫相圖，找出最吻合實驗的結果。
為了和最近角解析光電子能譜的實驗結果做比較，我們的遠程反鐵磁金屬態的結果得到了定性上相當類似的
能譜的摻雜趨勢以及其費米面。此外，能隙及能譜權值隨著摻雜的演化也將被詳細討論。

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.

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