2009/02/28 by E. J. Bergholtz, A. Karlhede · 1 citation
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1088/1742-5468/2009/04/p04015
published as J. Stat. Mech. (2009) P04015 · 12 pages, published
arxiv created 2009/04/21 · arxiv updated 2009/12/01
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.