Quantum Hall Circle

Details Quantum Hall Circle Quantum Hall Circle

2009-02-01

arxiv.org/abs/0902.0167v2

J. Stat. Mech. (2009) P04015

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, published

Scientific paper

10.1088/1742-5468/2009/04/P04015

We consider spin-polarized electrons in a single Landau level on a cylinder as the circumference of the cylinder goes to infinity. This gives a model of interacting electrons on a circle where the momenta of the particles are restricted and there is no kinetic energy. Quantum Hall states are exact ground states for appropriate short range interactions, and there is a gap to excitations. These states develop adiabatically from this one-dimensional quantum Hall circle to the bulk quantum Hall states and further on into the Tao-Thouless states as the circumference goes to zero. For low filling fractions a gapless state is formed which we suggest is connected to the Wigner crystal expected in the bulk.

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