Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems
arXiv:2507.00138 · doi:10.1063/5.0305441
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.
4+2 pages, a couple of figures
References in corpus (17)
- Non-Abelian Anyons and Topological Quantum Computation
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Observation of Fractionally Quantized Anomalous Hall Effect
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Colloquium: Quantum anomalous Hall effect
- Semiclassical theories of the anomalous Hall effect
- Geometric approach to fragile topology beyond symmetry indicators
- Berry's phase and the anomalous velocity of Bloch wavepackets
- Observation of the scaling dimension of fractional quantum Hall anyons
- Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
- Flux Quantization
- Topological Quantum Gates in Homotopy Type Theory
- Quantum Observables of Quantized Fluxes
- Topological insulators and geometry of vector bundles
- Engineering of Anyons on M5-Probes via Flux Quantization