Schreiber Type IIA Anyons

An article that we are writing at CQTS:

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• Nonabelian Anyons from Bounded Quantum Geometry

  manuscript: [to appear here]

Two-dimensional, two-band fractional Chern insulators (FCI) have recently been shown to admit abelian anyon statistics associated with momentum-space Bloch Hopfions. Here we show that bounding the integrated quantum metric along one primitive Brillouin-zone cycle—describing systems whose deformations explore only a bounded region of Bloch Hamiltonians—gives rise to $|C|$ distinct commuting braiding observables, cyclically permuted by lattice translations and jointly exhibiting nonabelian topological quantum order, for Chern numbers $|C| \gt 1$. We identify this cyclic structure with the spectral flow organizing hybrid Wannier states into the effective quantum Hall layers of Qi and Barkeshli, with the metric bound controlling the states’ real-space spread. Our results therefore exhibit a novel candidate realization of nonabelian topological order within the known orbital structure of FCIs, potentially informing experimental searches towards hardware for topological quantum processors.

• Based on:

  • Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems

  • On the Derivation of Twisted K-Theory from M-Theory