J_1-J_2团簇的数值模拟研究

NUMERICAL SIMULATION OF J _1-J_2 CLUSTERS

采用严格对角化方法计算了由几十个格点自旋构成的量子自旋团簇的基态总自旋 .在无阻挫情形 ,基态总自旋并不等于团簇的最低可能总自旋 ,而是取一个较大的值 .这意味着即使对于具有纳米尺寸的团簇 ,量子涨落也不破坏基态的经典奈尔序 .若在团簇中引入阻挫 ,则将诱导从奈尔序到自旋无序的量子相变 ,该相变可以通过基态总自旋的变化进行描述和标记 .计算表明 ,由于在相变点存在能级交错 ,故该量子相变应该是一级相变 .从团簇的数值计算结果可以推断 :对于二维无限 J1-J2 模型 ,临界点在 J2 / J1=0 .3 762 (± 0 .0 0 0 2 )处 .这一结果比以前的解析近似研究和有限系统标度分析的结果更为精确 .

For the quantum spin clusters of tens of sites, this paper calculates the total spin of ground state by exact diagonalization. In the non frustrated case, the ground state total spin takes not the lowest possible total spin but a higher value. It means the existence of Neél order in the ground state even for the clusters of nano scale. If introducing frustrations into clusters, it can induce a quantum phase transition from Neél order to spin disorder. This transition can be described and marked through the change of the ground state total spin. Calculations show that it should be the first order transition since the existence of level crossing at the critical J 2/J 1. From the numerical results of clusters, it can be inferred that for the infinite two dimensional J 1 J 2 model, the critical J 2/J 1 should be equal to 0 376 2 (±0.000 2). This result is more accurate than the previous data by analytical approximations and scaling analysis based on finite systems.