论文标题
在没有区域法纠缠的分形格子上的劳林拓扑
Laughlin topology on fractal lattices without area law entanglement
论文作者
论文摘要
Laughlin国家最近是在分形晶格上构建的，用于确认这些州具有Laughlin Type拓扑的指控和编织统计数据。在这里，我们研究了状态的密度，相关性和纠缠性能在源自sierpinski三角形的分形晶格上，目的是与二维系统相比，目的是识别相似性和差异，目的是研究各种分形晶格的拓扑探针。与二维系统类似，我们发现连接的粒子粒子相关函数与二维平面测量的晶格位点之间的距离大致衰减，但值也取决于局部环境。与二维系统相反，我们发现，如果将面积定义为越过所选子系统边缘的最近邻居债券的数量，则纠缠熵不会遵循该区域定律。考虑到具有两个键交叉的两部分，我们发现纠缠熵的对数缩放率与子系统中的位点数量。这也意味着不能使用Kitaev-Preskill或Levin-Wen方法提取拓扑纠缠熵。在研究不同两部分的纠缠频谱时，我们发现纠缠差距下方的状态数量稳健，并且与二维晶格的Laughlin国家相同。
Laughlin states have recently been constructed on fractal lattices, and the charge and braiding statistics of the quasiholes were used to confirm that these states have Laughlin type topology. Here, we investigate density, correlation, and entanglement properties of the states on a fractal lattice derived from a Sierpinski triangle with the purpose of identifying similarities and differences compared to two-dimensional systems and with the purpose of investigating whether various probes of topology work for fractal lattices. Similarly to two-dimensional systems, we find that the connected particle-particle correlation function decays roughly exponentially with the distance between the lattice sites measured in the two-dimensional plane, but the values also depend on the local environment. Contrary to two-dimensional systems, we find that the entanglement entropy does not follow the area law if one defines the area to be the number of nearest neighbor bonds that cross the edge of the selected subsystem. Considering bipartitions with two bonds crossing the edge, we find a close to logarithmic scaling of the entanglement entropy with the number of sites in the subsystem. This also means that the topological entanglement entropy cannot be extracted using the Kitaev-Preskill or the Levin-Wen methods. Studying the entanglement spectrum for different bipartitions, we find that the number of states below the entanglement gap is robust and the same as for Laughlin states on two-dimensional lattices.
