Quantum Hall Circle
Mesoscale and Nanoscale Physics
2009-04-21 v2 Strongly Correlated Electrons
Abstract
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.
Cite
@article{arxiv.0902.0167,
title = {Quantum Hall Circle},
author = {E. J. Bergholtz and A. Karlhede},
journal= {arXiv preprint arXiv:0902.0167},
year = {2009}
}
Comments
12 pages, published