The main results suggest that fragile band topology in fractional Chern insulators influences the observable anyonic topological order in fractional quantum Hall systems, highlighted by unique braiding phases of anyons.
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Effect estimate: null (95% CI null)
p-value: p=null
Recently observed fractional quantum anomalous Hall (FQAH) materials 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 L. Larmore and E. Thomas, Math. Scand. 47, 232 (1980), identifies FQAH anyons over momentum space. Admissible braiding phases involve 2C-th roots of unity, with 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.
Sati et al. (Mon,) conducted a null in fractional quantum anomalous Hall systems. null vs. null was evaluated on Anyonic topological order in fractional quantum anomalous Hall systems (null, 95% CI null, p=null). The main results suggest that fragile band topology in fractional Chern insulators influences the observable anyonic topological order in fractional quantum Hall systems, highlighted by unique braiding phases of anyons.