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Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model
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abstract
The 2-d $O(3)$-model with a $\theta$-vacuum term is formulated in terms of Wolff clusters. Each cluster carries a half-integer topological charge. The clusters with charge $\pm 1/2$ are identified as merons. At $\theta = \pi$ the merons are bound in pairs inducing a second order phase transition at which the mass-gap vanishes. The construction of an improved estimator for the topological charge distribution makes numerical simulations of the phase transition feasible. The measured critical exponents agree with those of the $k = 1$ Wess-Zumino-Novikov-Witten model. Our results are consistent with Haldane's conjecture for 1-d antiferromagnetic quantum spin chains.
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Cited by 1 Pith paper
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Phase structure analysis of CP(1) model with $\theta$ term by tensor renormalization group
Numerical tensor-network results locate a critical point at theta=pi in the 2D CP(1) model, consistent with Haldane's conjecture.
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