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

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.

18 pages, 8 figures, accepted version

References in corpus (31)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Non-Hermitian topological phenomena: A review
• Topological Non-Hermitian skin effect
• Topological Euler class as a dynamical observable in optical lattices
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Higher-order topological phases on fractal lattices
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Hermitian Floquet Topological Matter -- A Review
• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Symmetry and topological classification of Floquet non-Hermitian systems
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Optical manifestations and bounds of topological Euler class
• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Qubit-controlled directional edge states in waveguide QED
• Synthetic non-Abelian topological charges in ultracold atomic gases
• Gapless higher-order topology and corner states in Floquet systems
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Generalized Landau Paradigm for quantum phases and phase transitions
• Classification of unitary operators by local generatability
• Floquet Möbius topological insulators
• Robust qubit interactions mediated by photonic topological edge states