Cluster Algorithms For Anisotropic Quantum Spin Models

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.

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

References in corpus (3)

• Cluster Algorithm for Vertex Models
• Loop algorithms for quantum simulations of fermion models on lattices
• Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,

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• Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model
• Kosterlitz-Thouless transition of quantum XY model in two dimensions
• Directed-loop Monte Carlo simulations of vertex models
• The Two-Dimensional S=1 Quantum Heisenberg Antiferromagnet at Finite Temperatures
• Geometry, thermodynamics, and finite-size corrections in the critical Potts model
• Dynamic Monte Carlo Study of the Two-Dimensional Quantum XY Model
• Quantum Monte Carlo Loop Algorithm for the t-J Model
• Quantum Monte Carlo Annealing with Multi-Spin Dynamics