2025/05/28 by Hisham Sati, Urs Schreiber, Sati, Hisham +1 · 2 citations
Physics and Astronomy · #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2505.22144
openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.