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

• URL: http://arxiv.org/abs/2204.03834v2
• Date: Wed, 21 Sep 2022 08:39:16 GMT
• Title: Correspondence of topological classification between quantum graph extra dimension and topological matter
• Authors: Tomonori Inoue, Makoto Sakamoto, Masatoshi Sato, and Inori Ueba
• Abstract summary: We study five-dimensional Dirac fermions of which extra-dimension is compactified on quantum graphs. We provide a complete topological classification of the boundary conditions in terms of non-interacting fermionic topological phases.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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