论文标题
在Kagome晶格上网络模型中整数量子厅过渡的临界行为
Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice
论文作者
论文摘要
我们研究了Kagome晶格（NMKL）的网络模型。该模型概括了整数量子厅过渡的Chalker-Coddington（CC）网络模型。与我们之前研究的随机网络模型不同，Kagome晶格的几何形状是常规的。因此，我们期望NMKL的关键行为应与CC模型相同。我们在数值上计算NKML中的本地化索引$ν$。我们的结果$ν= 2.658 \ pm 0.046 $接近在许多最近的论文中获得的CC模型值。我们还将NMKL映射到随机电位和固定周期性曲率背景下的Dirac费米子。背景证明在长尺度上无关紧要。我们的数值和分析结果证实了我们对常规网络模型中关键行为普遍性的期望。
We study a network model on the Kagome lattice (NMKL). This model generalizes the Chalker-Coddington (CC) network model for the integer quantum Hall transition. Unlike random network models we studied earlier, the geometry of the Kagome lattice is regular. Therefore, we expect that the critical behavior of the NMKL should be the same as that of the CC model. We numerically compute the localization length index $ν$ in the NKML. Our result $ν= 2.658 \pm 0.046$ is close to CC model values obtained in a number of recent papers. We also map the NMKL to the Dirac fermions in random potentials and in a fixed periodic curvature background. The background turns out irrelevant at long scales. Our numerical and analytical results confirm our expectation of the universality of critical behavior on regular network models.
