Schreiber FQH Anyons (Rev #101, changes)

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An article that we are finalizing at CQTS:

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• Hisham Sati $\;\;\;$and$\;\;\;$ Urs Schreiber:

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  Fractional Quantum Hall Anyons

  via the Algebraic Topology of exotic Flux Quanta

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  download:

  • pdf (v3, additions and revisions)

  • arXiv:2505.22144 (v2)

Abstract. Fractional quantum Hall systems (FQH), due to their experimentally observed anyonic topological order, are a main contender for future hardware-implementation of error-protected quantum registers (“topological qbits”) subject to error-protected quantum operations (“topological quantum gates”), both plausibly necessary for future quantum computers at a useful scale, but both remaining insufficiently understood.

Here we present a novel non-Lagrangian effective description of FQH anyons, based on previously elusive proper global quantization of effective topological flux in extraordinary non-abelian cohomology theories. This directly translates the system’s quantum-observables, -states, -symmetries, and -measurement channels into purely algebro-topological analysis of local systems of Hilbert spaces over the quantized flux moduli spaces.

Under the hypothesis — for which we provide a fair bit of evidence — that the appropriate effective flux quantization of FQH systems is in 2-Cohomotopy (a cousin of Hypothesis H in high energy physics), the results here are rigorously derived and as such might usefully inform future laboratory searches for novel anyonic phenomena in FQH systems and hence for topological quantum hardware.

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Exposition in:

• Rethinking FQH Anyons (talk)

• Rethinking Topological Quantum (lightning talk)

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Based on:

• Flux Quantization

• Flux Quantization on M5-Branes

• Cohomotopy, Framed Links, and Abelian Anyons

• Anyons on M5-Probes of Seifert 3-Orbifolds

  (which in turn is based on: The Character Map in Twisted Equivariant Nonabelian Cohomology)

• Engineering of Anyons on M5-Probes via Flux-Quantization

  (lecture notes)

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Followup articles:

• Nonabelian Anyons attached to Superconducting Islands in FQH Liquids

• Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems

• Higher-dimensional Anyons via Higher Cohomotopy

• Non-Perturbative SDiff Covariance of FQH Excitations

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Related presentations:

• Homotopy Theory for Topological Quantum Computing

• Rethinking FQH Anyons -- talk

• Non-Lagrangian construction of abelian CS/FQH theory

• The $1 Million Puzzle: Hadrons and Quantum Computers

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