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Progress of Theoretical Physics

A Modified Decoupled Cell Method of Quantum Monte Carlo Calculation

Sanzo Miyazawa, Seiji Miyashita, M. S. Makivić, Shigeo Homma

Published Jun 1, 1993• 12 citations
Publisher

Abstract

A modified Decoupled Cell Method (mDCM) for quantum Monte Carlo simulation is proposed to remove the difficulty in the Decoupled Cell Method (DCM), which causes a negative specific heat and an unexpected sudden increase of a susceptibility in a low temperature region. In one-dimensional XY-model (s = 1/2), the results obtained by mDCM were shown not to have any negative specific heat and for the susceptibility along z-axis, gave fairly good agreement with the exact one.

DOI
10.1143/ptp.89.1167

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A modified Decoupled Cell Method (mDCM) for quantum Monte Carlo simulation is proposed to remove the difficulty in the Decoupled Cell Method (DCM), which causes a negative specific heat and an unexpected sudden increase of a susceptibility in a low temperature region. In one-dimensional XY-model (s = 1/2), the results obtained by mDCM were shown not to have any negative specific heat and for the susceptibility along z-axis, gave fairly good agreement with the exact one.
The properties of the spin-1/2 Heisenberg model on 1, 2, and 3-dimensional lattices are calculated using the Decoupled Cell Method of Homma et al., and these results are compared with high temperature and spin-wave expansions, and with other numerical approaches. The DCM has advantages over other Monte Carlo methods currently in wide use in that the transition probability is positive definite, there is no need to introduce an additional imaginary time, or Trotter, dimension, and the acceptance rate for transitions is comparable to that of classical lattice models. We find very good agreement between the DCM and the high temperature expansion in the temperature region where the high temperature expansion is valid, and reasonably good agreement at low temperatures with spin wave theory. The DCM fails for temperatures T < Tc which decreases with the size of the cell.
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.
The Antiferromagnetic Heisenberg Model with spin 1/2 on a square lattice was simulated by using the Stochastic Series Expansion(SSE) Quantum Monte Carlo Method.The temperature dependence of the internal energy,specific heat and uniform susceptibility was observed.The results showed that specific heat has a maximum at kT/J=0.6 and uniform susceptibility saturates at kT/J=1 for the isotropy case.And the size of lattice also affects the temperature dependence of these thermodynamic quantities.For the anisotropy case,energy decreases with anisotropic parameter g increasing.Susceptibility changes slowly with temperature for g1 and exponentially decay for g1 in the low temperature region and its behaviors approach consistent for different g in the high temperature region.