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arXiv · 2004.06666

Fractional Quantum Numbers, Complex Orbifolds and Noncommutative Geometry

Varghese Mathai·Graeme Wilkin
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Abstract

This paper studies the conductance on the universal homology covering space $Z$ of 2D orbifolds in a strong magnetic field, thereby removing the integrality constraint on the magnetic field in earlier works in the literature. We consider a natural Landau Hamiltonian on $Z$ and show that its low-lying spectrum consists of a finite number of isolated points. We 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.

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Varghese Mathai, Graeme Wilkin. 2020-04-14. Fractional Quantum Numbers, Complex Orbifolds and Noncommutative Geometry. https://doi.org/10.1088/1751-8121%2Fac0b8c

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