Correspondence of topological classification between quantum graph extra dimension and topological matter

• Published in: arXiv.org
• Main Authors: Inoue, Tomonori, Sakamoto, Makoto, Sato, Masatoshi, Ueba, Inori
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 21.09.2022
• Subjects: Boundary conditions; Classification; Fermions; Matrices (mathematics); Physics - High Energy Physics - Theory; Physics - Mesoscale and Nanoscale Physics; Physics - Quantum Physics; Symmetry; Topology
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2204.03834

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.