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Progress of Theoretical Physics Supplement

Quantum Cluster Algorithm Monte Carlo Method and Its Application to Higher-Spin Heisenberg Antiferromagnets

Synge Todo

Published Jan 1, 2002• 3 citations
Publisher

Abstract

The quantum Monte Carlo technique for quantum magnets has been greatly improved during the last decade. In this paper, we review the quantum cluster algorithm (loop algorithm) for higher-spin Heisenberg antiferromagnets, together with some technical aspects including parallelization technique and with its application to low-dimensional Heisenberg antiferromagnets.

DOI
10.1143/ptps.145.188

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The quantum Monte Carlo technique for quantum magnets has been greatly improved during the last decade. In this paper, we review the quantum cluster algorithm (loop algorithm) for higher-spin Heisenberg antiferromagnets, together with some technical aspects including parallelization technique and with its application to low-dimensional Heisenberg antiferromagnets.
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A cluster update (the ``operator loop'') is developed within the framework of a numerically exact quantum Monte Carlo method based on the power series expansion of $\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}H)$ (stochastic series expansion). The method is generally applicable to a wide class of lattice Hamiltonians for which the expansion is positive definite. For some important models the operator-loop algorithm is more efficient than loop updates previously developed for ``worldline'' simulations. The method is here tested on a two-dimensional anisotropic Heisenberg antiferromagnet in a magnetic field.
A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of inefficiency of the update of the total magnetization. The method is demonstrated in the one dimensional antiferromagnetic Heisenberg model and the trimer model. We attempted various other Monte Carlo algorithms to study systems in the external field and compared their efficiency.