Monte Carlo Studies of Quantum Spin Systems

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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.