Schreiber FQAH Anyons
An article that we are preparing at CQTS:
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Fractional Quantum Anomalous Hall Anyons
as Exotic Flux Quanta in Momentum Space
draft: [to appear here]
Abstract. The recently observed fractional quantum anomalous Hall materials (FQAH) have striking potential as topological quantum hardware at more practical conditions than ordinary FQH systems. However, the nature and potential control of their topological anyon states remains somewhat elusive.
Based on the observation that the FQAH effect appears like a momentum space dual of the FQH effect, and re-analyzing the fragile topology of its electron bands, we argue that FQAH anyons must be described by the recently discovered non-Lagrangian effective anyon quantum field theory via exotic flux quantization in 2-Cohomotopy, but now applied to the Berry flux in momentum space.
This description immediately generalizes to the subtle but important case of crystalline symmetry-protection and amounts to refining the topological phase classification from orbifold K-theory to tangentially twisted orbifold Cohomotopy of the Brillouin torus, through a twisted equivariant Boardman homomorphism which we construct.
Besides making predictions about fractional statistics and modular-equivariant topological order realizable in FQAH systems, this approach makes a clear prediction of FQAH anyons localized not in position space but in the reciprocal space of crystal quasi-momenta. We close with an outlook on their potential external adiabatic control for the purpose of implementing topologically protected quantum gates.
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Created on June 12, 2025 at 08:25:15. See the history of this page for a list of all contributions to it.