论文标题
量子图之间拓扑分类的对应关系额外的维度和拓扑问题
Correspondence of topological classification between quantum graph extra dimension and topological matter
论文作者
论文摘要
在本文中，我们研究了五维狄拉克式，其中量子图在量子图上被压缩。我们发现，在量子图的顶点上指定边界条件的矩阵之间存在非平凡的对应关系，而自由雕刻系统中的零维汉顿却是零维汉密尔顿人。基于对应关系，我们就非交互式的费米子拓扑阶段提供了边界条件的完整拓扑分类。拓扑阶段的十个对称类别用五维迪拉克费米斯的语言充分识别，并给出了边界条件的拓扑数。与非交互式费米子拓扑阶段中的块状对应关系类似，边界条件拓扑数可以预测位于量子图的顶点的四维无质量质量费米子，因此在四个维度中控制了低能物理学。
In this paper, we study five-dimensional Dirac fermions of which extra-dimension is compactified on quantum graphs. We find that there is a non-trivial correspondence between matrices specifying boundary conditions at the vertex of the quantum graphs and zero-dimensional Hamiltonians in gapped free-fermion systems. Based on the correspondence, we provide a complete topological classification of the boundary conditions in terms of non-interacting fermionic topological phases. The ten symmetry classes of topological phases are fully identified in the language of five-dimensional Dirac fermions, and topological numbers of the boundary conditions are given. In analogy with the bulk-boundary correspondence in non-interacting fermionic topological phases, the boundary condition topological numbers predict four-dimensional massless fermions localized at the vertex of the quantum graphs and thus govern the low energy physics in four dimensions.
