Fractional Quantum Hall Anyons via the Algebraic Topology of Exotic Flux Quanta
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908430332067840 |
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| author | Sati, Hisham Schreiber, Urs |
| author_facet | Sati, Hisham Schreiber, Urs |
| contents | 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 computing at 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 theory (a cousin of Hypothesis H in high-energy physics), the results here are rigorously derived and as such might usefully inform laboratory searches for novel anyonic phenomena in FQH systems and hence for topological quantum hardware. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22144 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Quantum Hall Anyons via the Algebraic Topology of Exotic Flux Quanta Sati, Hisham Schreiber, Urs Mesoscale and Nanoscale Physics Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Algebraic Topology 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 computing at 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 theory (a cousin of Hypothesis H in high-energy physics), the results here are rigorously derived and as such might usefully inform laboratory searches for novel anyonic phenomena in FQH systems and hence for topological quantum hardware. |
| title | Fractional Quantum Hall Anyons via the Algebraic Topology of Exotic Flux Quanta |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Algebraic Topology |
| url | https://arxiv.org/abs/2505.22144 |