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Progress of Theoretical Physics Supplement

Decoupled Cell Monte Carlo Method for Quantum Spin Systems on Linear Chain and on Triangular Lattice

Shigeo Homma, Kazuhiro Sano, Hirotsugu Matsuda, N. Ogita

Published Jan 1, 1986• 9 citations
Publisher

Abstract

Decoupled cell method is introduced as a method of Monte Carlo simulation for quantum spin systems. Based on this method we calculated the thermodynamic quantities such as an internal energy, in-plane and out-of-plane susceptibilities and spin-spin correlation functions in one dimensional XY model. The agreement with the exact results is excellent above a certain demarcation temperature. This method is also applied to the antiferromagnetic Heisenberg model on the triangular lattice. The results indicate the existence of a sublattice structure composed of three sublattices, although its spatial and temporal behaviours are short ranged.

DOI
10.1143/ptps.87.127

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Journal of the Physical Society of Japan•May 1, 1983•61 citations
Decoupled cell method is introduced as a method of Monte Carlo simulation for quantum spin systems. Based on this method we calculated the thermodynamic quantities such as an internal energy, in-plane and out-of-plane susceptibilities and spin-spin correlation functions in one dimensional XY model. The agreement with the exact results is excellent above a certain demarcation temperature. This method is also applied to the antiferromagnetic Heisenberg model on the triangular lattice. The results indicate the existence of a sublattice structure composed of three sublattices, although its spatial and temporal behaviours are short ranged.
Thermodynamic properties of antiferromagnetic quantum X Y -model ( s =1/2) on a triangular lattice are studied by the Decoupled Cell Monte Carlo Method (DCM). The decoupled cell (DC) used in this study consists of 7 spins. The size N of systems are 15 * 15, 30 * 30, 45 * 45, respectively. Detailed studies of spin pair correlation functions for both x - and z -components are performed at various temperatures. The results suggest that the existence of the shortrange three sublattice structure. The mean square magnetization of a sublattice for the x -component does not depend on N , whereas that of the z -component shows a strong dependence on N below a certain temperature.
The three-dimensional spin-1/2 Heisenberg model on a simple cubic lattice is studied for ferromagnetic and antiferromagnetic interactions using the Decoupled Cell Method for quantum Monte Carlo. Results for the relaxation time τL are determined for both ferromagnetic and antiferromagnetic systems and found to be similar to those found for the classical (s → ∞) Heisenberg model. The scaling of τL with system size is used to extract the dynamical critical exponent z for the two systems. The values of z = 1.98 ± 0.12 for the ferromagnet and z = 1.94 ± 0.09 for the antiferromagnet are in good agreement with theoretical predictions and previous Monte Carlo studies of the classical Heisenberg model.
Monte Carlo simulations of the Ising model on the triangular lattice with the antiferromagnetic nn interaction J and the ferromagnetic nnn interaction J ' are carried out. Several physical quantities (magnetizations, energies, susceptibilities, specific heats of sublattices and of the total system) are calculated. A phase which resembles the partially disordered phase proposed by Mekata is observed in the finite temperature region. But it is shown in this region that the sublattice magnetizations vanish at the thermodynamic limit and the Kosterlitz-Thouless phase transition is predicted by the finite size analysis.