Schreiber QMATH16

A talk that I will have given:

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• Urs Schreiber$\;\;$ on joint work with $\;\;$ Hisham Sati:

  
  

  Identifying Anyonic Topological Order in

  Fractional Quantum Anomalous Hall Systems

  slides: [to appear here]

• talk at:

  QMATH16, Munich (1-5 Sept 2025)

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Based on:

• Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems [pdf, arXiv:2507.00138]

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 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.

Related presentations:

• at ISQS29 (brief talk)

• Rethinking Topological Quantum (lightning talk)

• Rethinking FQH Anyons (talk)

• Engineering of Anyons on M5-Probes (lecture series)