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The Landau Problem on the θ-Deformed Two-Torus

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Abstract

We study the Landau problem on the θ-deformed two-torus and use well-known projective modules to obtain perturbed energy spectra. For a strong magnetic field B, the problem can be restricted to one particular Landau level. First we represent generators of the algebra of the noncommutative torus T θ  2 as finite-dimensional matrices. A second approach leads to a reducible representation with a θ-dependent center. For a simple periodic potential, the rational part of the Hofstadter butterfly spectrum is obtained.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Vienna, Boltzmanngasse 5, 1090, Wien, Austria

    H. Grosse & M. Kornexl

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  1. H. Grosse
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  2. M. Kornexl
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Grosse, H., Kornexl, M. The Landau Problem on the θ-Deformed Two-Torus. Letters in Mathematical Physics 63, 73–83 (2003). https://doi.org/10.1023/A:1022922410256

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