${\mathbb C} P^{N-1}$在${\mathbb R} \乘以S^1$上的扭曲${\mathbb C}模型的格研究

T. Misumi, T. Fujimori, E. Itou, M. Nitta, N. Sakai
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引用次数: 3

摘要

我们在$S_{s}^{1}$(大)$\times$$S_{\tau}^{1}$(小)上报告了${\mathbb C} P^{N-1}$ sigma模型的晶格模拟结果。我们取足够大的周长比例来近似${\mathbb R} \times S^1$上的模型。对于施加于$S_{\tau}^{1}$方向的周期边界条件,我们表明,随着紧化周长的减小,Polyakov环的期望值经历了一个去定义交叉,其中相关磁化率的峰值随着$N$的增大而变得更加明显。对于${\mathbb Z}_{N}$扭曲边界条件,我们发现,即使在较高的$\beta$(小周长)下,Polyakov环的规则的$N$边多边形分布导致Polyakov环的期望值较小,这意味着如果采用足够的统计量和大体积,则不破坏${\mathbb Z}_{N}$对称性。我们还通过研究Polyakov环对$S_{s}^{1}$方向的依赖,论证了分数瞬子和十亿子的存在性,这导致了${\mathbb Z}_{N}$真空之间的跃迁。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Lattice study on the twisted ${\mathbb C} P^{N-1}$ models on ${\mathbb R} \times S^1$
We report the results of the lattice simulation of the ${\mathbb C} P^{N-1}$ sigma model on $S_{s}^{1}$(large) $\times$ $S_{\tau}^{1}$(small). We take a sufficiently large ratio of the circumferences to approximate the model on ${\mathbb R} \times S^1$. For periodic boundary condition imposed in the $S_{\tau}^{1}$ direction, we show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as the compactified circumference is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. For ${\mathbb Z}_{N}$ twisted boundary condition, we find that, even at relatively high $\beta$ (small circumference), the regular $N$-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ${\mathbb Z}_{N}$ symmetry if sufficient statistics and large volumes are adopted. We also argue the existence of fractional instantons and bions by investigating the dependence of the Polyakov loop on $S_{s}^{1}$ direction, which causes transition between ${\mathbb Z}_{N}$ vacua.
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