Monte Carlo Studies of Quantum Spin Systems

本文提出了一种新的量子多体系统蒙特卡罗计算方法--解耦胞腔蒙特卡罗方法（DCM）。我们将DCM应用于二维量子自旋系统：（I）正方晶格上的XY自旋模型（s=1/）和（II）三角晶格上的反铁磁XY自旋模型（s=1/）。结果如下。对于情形（I），存在一个类似于相应经典模型的KT相变。然而，对于量子情况下的跃迁性质，我们在高温相的蒙特卡罗结果似乎与关联长度（T）的幂律奇异性相容<zeta>。临界指数<nu>，<gamma>并<eta>在过渡点分别为1.0，1.6 - <plus-minus>0.1和0.4 <plus-minus>- 0.1。这些值是通过计算微观热力学量独立获得的。这些<nu>，<gamma>并<eta>满足比例关系（2-<eta>）<nu>=<gamma>。对于情形（II），我们没有发现热力学量对温度T的奇异行为。这意味着在该模型系统中不发生相变。对自旋x和z分量的空间自旋对关联函数C^x（r）和C^z（r）的观测表明，在自旋x和z分量中存在三个亚晶格结构，但这些关联函数随r的增大呈指数衰减。假设相关长度<zeta>^x（T）和<zeta>^z（T）在T= 0 K处保持有限。这意味着这样获得的亚晶格结构即使在T= 0 K时也保持短程。这与相应的经典系统相反，其中通过计算机模拟观察到急剧的转变。量子效应抑制了导致经典体系长程亚晶格结构形成的挫折。

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.