Model for the fractional quantum Hall effect problem

M.I. Dyakonov

doi:doi:10.1051/jp4:20020441

Issue		J. Phys. IV France Volume 12, Number 9, November 2002


Page(s)		373 - 376
DOI		https://doi.org/10.1051/jp4:20020441

J. Phys. IV France 12 (2002) Pr9-373
DOI: 10.1051/jp4:20020441

Model for the fractional quantum Hall effect problem

M.I. Dyakonov

Laboratoire de Physique Mathématique et Théorique, Université Montpellier 11, place E. Bataillon, 34095 Montpellier, France

Abstract
A simple one-dimensional model is proposed, in which N spinless interacting fermions occupy M>N degenerate states on a circle. It is argued that the energy spectrum and the wavefunctions of this system strongly resemble the spectrum and wavefunctions of 2D electrons in the lowest Landau level (the problem of the Fractional Quantum Hall Effect). In particular, Laughlin-type wavefunctions describe ground states at filling factors $\nu N/M=1/(2m+1)$ . Within this model the complimentary wavefunction for $\nu =l-I/(2m+1)$ is found explicitly.