本計畫主要目的為，以?值方法對高溫超導體??之「t-J?模型」基態性質作一有系統的研究。在最佳摻雜（optimal doped）或是過?摻雜（overdoped）的?態下，現有??已經可以大致解釋實驗所觀察得的現象，然而低?摻雜（underdoped）的高溫超導體有許多特性，仍然難以解釋，?如：當載?子（可能為電子或是電?）逐漸增加，銅氧平面由反鐵磁相之Mott insulator至超導相之間的變化；費米面之形?；膺能隙（pseudogap）與超導長程序；以及條紋相（stripe phase）等問題。由於此?模型屬於「強關?電子系統」，無法以傳統?子?學的微擾法逼近求解，因此有必要借助?值方法，才能得到可靠的結果。本計畫除?用現有的?子蒙地卡?方法，計算此?系統之能?、自旋結構相關函?、電荷結構相關函?、配對相關函?、電?相關函?以及動?分佈函?等基態時的物??，藉此進?在各??範圍（指?同的電子密?Ne以及耦合強?J/t）的性質之外，也將開發?強?的?值方法，以期以有限的計算資源求得??確的結果，並能將新的?值方法應用於其他凝態物?模型之上。 In the project, the ground state properties of the t-J type models for High-Tc superconductivity will be studied by numerical methods in a systematical way. For optimal doped and overdoped cases, the theories can explain the experimental observations well. But for uderdoped High-Tc superconductors, several properties are still in puzzle. For example, it is still controversial for the mechanism of the transition from Mott insulator to superconductor as the doped hole density is increased. Other questions like the shape of the Fermi surface, the relation between pseudogap and superconducting long-range order, and stripe phase are still not fully resolved. The t-J type models are "strongly-correlated electron systems" and cannot be solved by the traditional perturbation method. Thus accurate numerical methods are necessary to resolve this kind of questions. In this project, the quantum Monte Carlo method will be used to calculate the energy, spin and charge correlation functions, pair-pair correlation function, current-current correlation function, and momentum distribution function of the ground state of the models. The phases of different parameter spaces will be determined by these measured properties. In the mean time, we will develop more powerful numerical methods in order to yield more accurate results. And the new methods will be tried to apply on other condensed-matter models.
