Fractional quantum numbers, complex orbifolds and noncommutative geometry

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This paper studies the conductance on the universal homology covering space Z of 2D orbifolds in a strong magnetic field, thereby removing the rationality constraint on the magnetic field in earlier works (Avron et al 1994 Phys. Rev. Lett. 73 3255–3257; Mathai and Wilkin 2019 Lett. Math. Phys. 109 2473–2484; Prieto 2006 Commun. Math. Phys. 265 373–396) in the literature. We consider a natural Landau Hamiltonian on Z and study its spectrum which we prove consists of a finite number of low-lying isolated points and calculate the von Neumann degree of the associated holomorphic spectral orbibundles when the magnetic field B is large, and obtain fractional quantum numbers as the conductance.
Original languageEnglish
Article number314001
Number of pages18
JournalJournal of Physics A: Mathematical and Theoretical
Publication statusPublished - 1 Jul 2021

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  • fractional quantum numbers
  • Riemann orbifolds
  • holomorphic orbibundles
  • von Neumann degree
  • noncommutative geometry

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