Non-Abelian topological charges determined by Euler class
Phys. Rev. A 114, 013515 – Published 15 July, 2026
DOI: https://doi.org/10.1103/kyzv-9lsh
Abstract
The interplay between multiple bands gives rise to non-Abelian defects, which are typically characterized by corresponding non-Abelian topological charges. Here we present a practical and intuitive approach for determining the non-Abelian topological charge of a defect based on its associated two-band Euler classes, without requiring knowledge of the Euler class of a defect pair. The approach is illustrated using a parity-time-symmetric tight-binding model that hosts braiding defects on a two-dimensional square lattice, and the resulting topological charges are consistent with those obtained from conventional spin Berry-Wilczek-Zee connection integrals. The factorization of the non-Abelian topological charge carried by a defect is naturally encoded in a set of two-band Euler classes, thereby elucidating the mechanism underlying defect formation.
