Coupled-wire construction of non-Abelian higher-order topological phases

• URL: http://arxiv.org/abs/2512.21179v2
• Date: Tue, 30 Dec 2025 07:05:47 GMT
• Title: Coupled-wire construction of non-Abelian higher-order topological phases
• Authors: Jiaxin Pan, Longwen Zhou,
• Abstract summary: This work extends the understanding of higher-order topological phases into non-Abelian regimes.<n>It suggests feasible experimental realizations in synthetic quantum systems, such as photonic or acoustic metamaterials.
• Score: 2.029444813790076
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host boundary states at corners or hinges, their characterization has largely relied on Abelian invariants such as winding and Chern numbers. Here, we propose a coupled-wire scheme of constructing non-Abelian HOTPs and analyze a non-Abelian second-order topological insulator as its minimal model. The resulting Hamiltonian supports hybridized corner modes, protected by parity-time-reversal plus sublattice symmetries and described by a topological vector that unites a non-Abelian quaternion charge with an Abelian winding number. Corner states emerge only when both invariants are nontrivial, whereas weak topological edge states of non-Abelian origins arise when the quaternion charge is nontrivial, enriching the bulk-edge-corner correspondence. The system further exhibits both non-Abelian and Abelian topological phase transitions, providing a unified platform that bridges these two distinct topological classes. Our work extends the understanding of HOTPs into non-Abelian regimes and suggests feasible experimental realizations in synthetic quantum systems, such as photonic or acoustic metamaterials.

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