标题： Meron-Cluster 在 2-d $O(3)$模型中的 $θ$真空模拟 显示英文标题

标题： Meron-Cluster Simulation of the $θ$-Vacuum in the 2-d $O(3)$-Model

摘要： 二维$O(3)$模型包含一个$\theta$真空项，该模型是用 Wolff 集群来表述的。 每个集群携带一个半整数拓扑电荷。 电荷为$\pm 1/2$的集群被识别为梅隆。 在$\theta = \pi$处，梅隆成对结合，在此发生二阶相变，此时质量间隙消失。 构建一个改进的拓扑电荷分布估计量使得对该相变的数值模拟成为可能。 测量得到的临界指数与$k = 1$Wess-Zumino-Novikov-Witten 模型的临界指数一致。 我们的结果与一维反铁磁量子自旋链的 Haldane 猜想一致。 显示英文摘要

摘要： 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.