Cluster Algorithms For Anisotropic Quantum Spin Models

TL;DR

This paper introduces efficient cluster Monte Carlo algorithms for anisotropic quantum spin models, notably reducing autocorrelation times and improving simulation efficiency for the $XYZ$ and $XY$ models.

Contribution

The authors develop novel cluster algorithms for $XYZ$ quantum spin models, including a special case for $S=1/2$ related to the 8-vertex model, with improved performance over traditional methods.

Findings

Autocorrelation time remains of order unity regardless of temperature, size, or Trotter number.

Conventional algorithms show autocorrelation times that increase with system parameters.

Improved estimators further enhance the efficiency of the new algorithms.

Abstract

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.