Lie algebra of DiffAT2and Bloch electrons in a constant uniform magnetic field
- 7 December 1993
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 26 (23) , 6961-6971
- https://doi.org/10.1088/0305-4470/26/23/035
Abstract
Magnetic translation operators that generate symmetries of a Bloch electron in a constant uniform magnetic field are shown to span the sine bracket algebra which is the unique Lie algebra deformation of the area-preserving diffeomorphisms of a two-torus. The deformation parameter is identified with the number of magnetic flux quanta through a unit cell of the substrate lattice. The symmetries of a spin-1/2 Bloch electron are shown to realize the supersymmetric extension of the sine bracket algebra.Keywords
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