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arXiv:2512.21179

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

Jiaxin Pan, Longwen Zhou

cond-mat.mes-hallquant-phSubmitted Dec 24, 2025• Announced Dec 25, 2025• Revised May 14, 2026 (v3)

v1 · Dec 24, 2025 v2 · Dec 30, 2025 v3 · May 14, 2026

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.

Journal reference: Phys. Rev. B 113, 195405 (2026)
DOI: 10.1103/kx2n-d3qs
Comments: 18 pages, 8 figures, accepted version

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Starting from an array of interacting fermionic quantum wires, we construct a family of non-Abelian topologically ordered states of matter in three spatial dimensions (3D). These states of matter inherit their non-Abelian topological properties from the

su(2)^{\,}_{k}

conformal field theories that characterize the constituent interacting quantum wires in the decoupled limit. Thus, the resulting topological phases can be viewed as 3D generalizations of the (bosonic)

su(2)^{\,}_{k}

Read-Rezayi sequence of fractional quantum Hall states. Focusing in detail on the

su(2)^{\,}_{2}

case, we first review how to determine the nature of the non-Abelian topological order (in particular, the topological degeneracy on the torus) in the two-dimensional (2D) case, before generalizing this approach to the 3D case. We also investigate the 2D boundary of the 3D phases, and show for the

su(2)^{\,}_{2}

case that there are anomalous gapless surface states protected by an analog of time-reversal symmetry, similar to the massless Dirac surface states of the noninteracting 3D topological insulator.