Cluster Algorithms For Anisotropic Quantum Spin Models

Details Cluster Algorithms For Anisotropic Quantum Spin Models Cluster Algorithms For Anisotropic Quantum Spin Models

1995-06-18

arxiv.org/abs/cond-mat/9506075v1

Physics

Condensed Matter

20 pages including 3 figures and 3 tables, accepted for publication in J. Stat. Phys

Scientific paper

10.1007/BF02189228

We present cluster Monte Carlo algorithms for the $XYZ$ quantum spin models. In the special case of $S=1/2$, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study the $S=1/2$ $XY$ model in two dimensions with a representation in which the quantization axis lies in the easy plane. We find that the numerical autocorrelation time for the cluster algorithm remains of the order of unity and does not show any significant dependence on the temperature, the system size, or the Trotter number. On the other hand, the autocorrelation time for the conventional algorithm strongly depends on these parameters and can be very large. The use of improved estimators for thermodynamic averages further enhances the efficiency of the new algorithms.

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