Schreiber Type IIA Anyons (Rev #3, changes)

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An article that we are writing at CQTS:

• Nonabelian Layered Hopf Anyons from in FCIs with Bounded Quantum Geometry

  manuscript: [to appear here]

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Two-dimensional, two-band fractional Chern insulators (FCI) have recently been shown to in principle admit unusual abeliananyon statistics associated with momentum-space Bloch Hopfions . Here localized we in show that bounding the integratedmomentum-space. Here we show that bounding the integrated quantum metric along one primitive Brillouin-zone cycle refines may refine this to$|C|$topological order distinct to commuting braiding$|C|$ distinct commuting braiding observables, cyclically permuted by lattice translations translations, and for jointly exhibiting nonabeliantopological quantum order, for Chern numbers $|C| \gt 1$ . We The identify this cyclic structure with matches thespectral flow organizing hybrid Wannier states into the effective quantum Hall layers of Qi and Barkeshli , with the metric bound being the states’ real-space spread. This We result observe points that, to for a novel candidate realization of$|C| = 2$, the resulting topological quantum gate set may contain the T-gate. This result points to 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.

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• Based on:

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

  • Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems

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