Schreiber FQAH Anyons

An article that we have written at CQTS:

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

  
  

  Identifying Anyonic Topological Order in

  Fractional Quantum Anomalous Hall Systems

  
  

  Applied Physics Letters

  128 023101 (2026)

  doi:10.1063/5.0305441

  
  

  in the special issue:
  Quantum Geometry in Condensed Matter: Fundamentals and Applications

  
  

  • download (4+2 pages):

    • pdf (v2: published version)

    • 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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Building on:

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

• Geometric Orbifold Cohomology

Talk presentations:

• at QMATH16

• at Bilkent25

Related talks:

• Geometric Orbifold Cohomology in Singular-Cohesive ∞-Topoi

Featured at QuantumZeitgeist:

Followups:

• Fragile Topological Phases and Topological Order of 2D Crystalline Chern Insulators

• Orientations of Orbi-K-Theory measuring Topological Phases and Brane Charges

  in: Geometric Orbifold Cohomology

• Drinfeld Center as Quantum State Monodromy over Bloch Hamiltonians around Defects