Schreiber FQAH Anyons

An article that we are finalizing at CQTS:

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• Hisham Sati$\;\;\;$and$\;\;\;$ Urs Schreiber:

  
  

  Identifying Anyonic Topological Order in

  Fractional Quantum Anomalous Hall Systems

  • download (4+2 pages):

    • pdf (v2: minor polishing)

    • arXiv:2507.00138

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 of 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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Based on:

• Fractional Quantum Hall Anyons via the Algebraic Topology of exotic Flux Quanta

• Geometric Orbifold Cohomology

Followup:

• Crystalline Chern Phases

Related talks:

• Geometric Orbifold Cohomology in Singular-Cohesive ∞-Topoi