Quantum Hall Dynamics on von Neumann Lattice

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dc.creatorIshikawa, K.
dc.creatorMaeda, N.
dc.creatorOchiai, T.
dc.creatorSuzuki, H.
dc.date1998-09-22
dc.date.accessioned2026-07-07T03:11:33Z
dc.date.available2026-07-07T03:11:33Z
dc.descriptionQuantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely the Hall conductance is the winding number of the propagator in the momentum space and is quantized exactly as integer multiple of ${e^2}/h$ in quantum Hall regime of the system of interactions and disorders. This shows that a determination of the fine structure constant from integer quantum Hall effect is in fact possible. We present also a unified mean field theory of the fractional Hall effect for the in-compressible quantum liquid states based on flux condensation and point out that the known Hofstadter butterfly spectrum of the tight binding model has a deep connection with the fractional Hall effect of the continuum electrons. Thus two of the most intriguing and important physical phenomena of recent years, the integer Hall effect and fractional Hall effect are studied and are solved partly by von Neumann lattice representation.
dc.descriptionRevTeX, 7 pages with 1 figure, to appear in the proceedings of International Conference on High Energy Physics, Vancouver, Canada, July 23-29, 1998
dc.identifierhttps://arxiv.org/abs/cond-mat/9809287
dc.identifierhttp://arxiv.org/abs/cond-mat/9809287
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/28613
dc.subjectMesoscale and Nanoscale Physics
dc.subjectHigh Energy Physics - Theory
dc.titleQuantum Hall Dynamics on von Neumann Lattice
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