Correspondence of topological classification between quantum graph extra dimension and topological matter
Correspondence of topological classification between quantum graph extra dimension and topological matter
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DOI：
10.1103/physrevd.106.085006
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发表时间：
2022-04
影响因子：
5
通讯作者：
Tomonori Inoue;M. Sakamoto;Masatoshi Sato;Inori Ueba
中科院分区：
文献类型：
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作者：
Tomonori Inoue;M. Sakamoto;Masatoshi Sato;Inori Ueba
本文研究了量子图上五维狄拉克费米子对称边界条件的分类。我们发现，在量子图顶点边界条件的分类与间隙自由费米子系统的对称保护拓扑相的分类之间存在非极小的对应关系，该系统被时间逆转对称、粒子空穴对称和手性对称划分为10个对称类。在我们的模型中指定边界条件的厄米矩阵对应于间隙自由费米子系统中的零维哈密顿矩阵。此外，模型中的对称性给出了约束边界条件参数空间的条件。这些条件与具有对称性的哈密顿量应该满足的间隙自由费米子系统中的条件相同。我们还表明，我们的模型中每个对称类的拓扑数意味着在量子图的顶点存在四维无质量场，就像来自体边界对应的自由费米子系统的无间隙边界态一样。
In this paper, we study a classification of boundary conditions with symmetries for a five-dimensional Dirac fermion on a quantum graph. We find that there is a nontrivial correspondence between the classification of boundary conditions at the vertex on the quantum graph and that of the symmetry-protected topological phases of gapped free-fermion systems, which are classified into ten symmetry classes by the time-reversal symmetry, particle-hole symmetry and chiral symmetry. A Hermitian matrix which specifies the boundary conditions in our model corresponds to a zero-dimensional Hamiltonian in the gapped free-fermion systems. Furthermore, symmetries in our model give the condition that restricts the parameter space of the boundary conditions. These conditions are identical to the ones in the gapped free-fermion systems that the Hamiltonian with the symmetries should satisfy. We also show that the topological number for each symmetry class in our model implies the presence of 4d massless fields localized at the vertex of the quantum graph, like gapless boundary states for the free-fermion systems from the bulk-boundary correspondence.