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Cluster algorithms for general-S quantum spin systems

Synge Todo·Kiyoshi Kato
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Abstract

We present a general strategy to extend quantum cluster algorithms for S=1/2 spin systems, such as the loop algorithm, to systems with arbitrary size of spins. In general, the partition function of a high-S spin system is represented in terms of the path integral of a S=1/2 model with special boundary conditions. We introduce additional graphs to be assigned to the boundary part and give the labeling probability explicitly, which completes the algorithm together with an existing S=1/2 cluster algorithm. As a demonstration of the algorithm, we simulate the the integer-spin antiferromagnetic Heisenberg chains. The magnitude of the first excitation gap is estimated as to be 0.41048(6), 0.08917(4), and 0.01002(3) for S=1, 2, and 3, respectively.

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Synge Todo, Kiyoshi Kato. 2001-05-30. Cluster algorithms for general-S quantum spin systems. https://doi.org/10.1103/physrevlett.87.047203

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