论文标题
$ν= 2/5 $和$ 3/7 $的Abelian拓扑顺序
Abelian topological order of $ν=2/5$ and $3/7$ fractional quantum Hall states in lattice models
论文作者
论文摘要
确定分数量子霍尔国家支持的基本激发的统计数据对于了解其性质和潜在应用至关重要。在本文中，我们使用拓扑纠缠熵作为Abelian统计数据的指标来研究乐队混合制度中Hofstadter模型的单组分$ν= 2/5 $和$ 3/7 $的状态。我们使用无限缸密度矩阵重新归一化组进行多体模拟，并提出有效的算法来构建纠缠区域定律，该定律既说明了数值和统计误差。使用此算法，我们表明$ν= 2/5 $和$ 3/7 $的州在两体邻次互动的情况下展示了Abelian拓扑订单。此外，我们讨论了所提出的方法和分数量子霍尔在相互作用范围和强度方面的敏感性。
Determining the statistics of elementary excitations supported by fractional quantum Hall states is crucial to understanding their properties and potential applications. In this paper, we use the topological entanglement entropy as an indicator of Abelian statistics to investigate the single-component $ν=2/5$ and $3/7$ states for the Hofstadter model in the band mixing regime. We perform many-body simulations using the infinite cylinder density matrix renormalization group and present an efficient algorithm to construct the area law of entanglement, which accounts for both numerical and statistical errors. Using this algorithm, we show that the $ν=2/5$ and $3/7$ states exhibit Abelian topological order in the case of two-body nearest-neighbor interactions. Moreover, we discuss the sensitivity of the proposed method and fractional quantum Hall states with respect to interaction range and strength.
