Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems

• URL: http://arxiv.org/abs/2507.00138v1
• Date: Mon, 30 Jun 2025 18:00:07 GMT
• Title: Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems
• Authors: Hisham Sati, Urs Schreiber,
• Abstract summary: Recently observed fractional quantum anomalous Hall materials (FQAH) are candidates for topological quantum hardware.<n>We point out dependence on monodromy in the fragile band topology in 2-cohomotopy.<n>An algebro-topological theorem of Larmore & Thomas (1980) then identifies FQAH anyons over momentum space.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently observed fractional quantum anomalous Hall materials (FQAH) are candidates for topological quantum hardware, but their required anyon states are elusive. We point out dependence on monodromy in the fragile band topology in 2-cohomotopy. An algebro-topological theorem of Larmore & Thomas (1980) then identifies FQAH anyons over momentum space. Admissible braiding phases are 2C-th roots of unity, for C the Chern number. This lays the foundation for understanding symmetry-protected topological order in FQAH systems, reducing the problem to computations in equivariant cohomotopy.

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