中文摘要：

利用Lanczos方法的TITPACK程序，计算了1维量子海森堡模型基态和低激发态波函数，能量的本征值和算符两点关联函数值与系统哈密顿量参数的变化关系。然后，用Matlab软件进行有限尺寸修正，基态能量计算值与理论值误差为0．0000472，而基态能量的绝对值与链长成平方反比关系E～1／n^2。在XXZ模型中粒子间距d与Sx、Sz算符两点关联函数值之间呈幂级数下降S=Aexp（-d／B）的规律。计算结果和Haldane提出的1维量子海森堡XXZ模型中基态和低激发态能量相符合，只有在耦合常数J等于某些值时有能级交叠。

英文摘要：

In this paper, the energy spectrum of the ground-state and the excited-state in the model of small size one- dimensional Heisenberg finite chains （n〈20） was discussed. The Complete Diagonal and Lanczos Iterative method of Hamiltonian matrix are actualized by TITPACK program which designed by Hidetoshi Nishimori. But the finite chain revised method is mainly actualized by MATLAB program. All programs would be given in this paper. The investigative object was small size one-dimensional Heisenherg finite chains （n〈20）, the TITPACK program was used to calculate the eigenvector of ground-state and excited-state｜ψ0〉, ｜ψ1〉,｜ψ2〉,｜ψ3〉, the energy eigenvalue of ground-state and excited-state λ0 ,λ1 ,λ2 λ3, the variation relation between and the correlated function of Sx, Sz and the system Hamilton parameter. Using the finite chain revised method, the error was 0. 000 047 2 between calculated and theoretic ground-state eigenvalue. The absolute value of ground-state energy square was inversed ratio the chain length, such as E（n）=0. 443 1-0. 848 4/n^2 , through analyze the result of the program and find the law between the result and the quantity, in the small size one-dimensional Heisenberg finite chains, S=Aexp（-d/B） in the XXZ model. It is completely difference with XXZ Quantum model presented by Haldane. Only some energy spectra were intersected.