本論文研究各種一維量子自旋模型的低能量性質。第一部份是研究沒有雜質的模型，如反鐵磁海森堡模型、交錯模型、J-J’模型。利用Householder method與Lanczos method，計算各模型的基態能量、第一激發態能量、自旋能隙，以及計算自旋關聯函數，再利用有限尺度分析外差求得熱力學極限值。第二部分是將自旋模型加入磁性或非磁性雜質，討論自旋關聯函數的變化。 In this article, we study one-dimensional quantum spin models, including S=1/2 Heisenberg model, alternating model and J-J’ model. Ground state energy, singlet-triplet energy gap and spin-spin correlation function are calculated by Householder and Lanczos method for finite-size systems. By extrapolating these results, the values of the above quantities at infinite-size limite are estimated. Finally we discuss the effect of magnetic and nonmagnetic impurities on the spin-spin correlations.
