Monte Carlo Studies of Quantum Spin Systems

作为量子多体系统蒙特卡罗计算的一种新方法，提出了“解耦单元蒙特卡罗方法”（DCM）。我们将DCM应用于二维量子自旋系统，(I)正方形晶格上的XY自旋模型（s=1/）和（II）三角形晶格上的反铁磁XY模型（s=1/）。结果如下。对于情形(I)，存在与相应经典模型的KT相变相似的相变。然而，对于量子跃迁的性质，我们在高温相的蒙特卡罗结果似乎与幂律奇点在相关长度<zeta>(T)下兼容。临界点<nu>, <gamma>, <eta>分别为1.0,1.6<正负>0.1,0.4<正负>0.1。这些数值是通过计算微观热力学量独立得出的。<nu>, <gamma>, <eta>满足缩放关系(2-<eta>) <nu> = <gamma>。对于情形（II），我们没有发现热力学量随温度t的奇异行为，这意味着在该模型系统中没有发生相变。对自旋x分量和z分量的空间自旋对相关函数(C^x（r)和C^z(r)）的观测表明，自旋x分量和z分量存在三个亚晶格结构，但这些相关函数随着r的增加呈指数衰减。相关长度<zeta>^x(T)和<zeta>^z(T)应该在T=OK时保持有限。这意味着这样得到的子晶格结构即使在T=OK时仍然是短距离的。这与相应的经典系统形成对比，在经典系统中，计算机模拟观察到一个急剧的转变。量子效应抑制了导致经典体系形成长程亚晶格结构的挫折。

We proposed 'Decoupled Cell Monte Carlo Method'(DCM) as a new method of Monte Carlo calculation for quantum many-body systems. We applied DCM to two-dimensional quantum spin systems, (I) XY spin model (s=1/)on the square lattice and (II) antiferromagnetic XY model (s=1/) on the triangular lattice. The results are the following. For the case (I)there exists a phase transiton similar to the KT transition of the corresponding classical model. However as to the nature of the transition in the quantum case our Monte Carlo results in the high-temperature phase seem compatible with power-law singularity in a correlation length <zeta>(T). Critical exponents <nu> , <gamma> and <eta> at the transition point are obtained as 1.0, 1.6<plus-minus> 0.1 and 0.4<plus-minus>0.1, respectively. These values are obtained independently through calculations of microscopic thermodynamic quantities. These <nu> , <gamma> and <eta> satisfy the scaling relation (2-<eta>) <nu> = <gamma> . For case (II) we could not find sigular behaviors of thermodynamic quantities in the dependence on temperature T. This means that there occurs no phase transition in this model system. Observations of spatial spin-pair correlation functions (C^x(r) and C^z(r) for x-and z-component of spin show that there exists three sublattice structure in x-and z-component of spin, but these correlation functions decays exponentially as r increases. Correlation length <zeta>^x(T) and <zeta>^z(T) are supposed to remain finite at T=OK. This means that the sublattice structure thus obtained remains short-ranged even at T=OK. This is contrast to the corresponding classical system, where a sharp transition was observed by computer simulation. The quantum effects suppress frustrations which is responsible to the formation of a long-ranged sublattice structure of the classical system.