One-dimensional model for the fractional quantum Hall effect

20th International Conference on the Application of High Magnetic Fields in Semiconductor Physics

Dyakonov, M.I.^1

Laboratoire Charles Coulomb, Université Montpellier II, CNRS, France^1

关键词: Degenerate state;    Energy spectra;    Filling factor;    Fractional quantum Hall effects;    Ground state wavefunctions;    Interacting fermions;    Landau levels;    One-dimensional model;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/456/1/012008/pdf
DOI  :  10.1088/1742-6596/456/1/012008

来源: IOP

【 摘 要 】

A simple one-dimensional model is proposed, in which N spinless repulsively interacting fermions occupy M>N degenerate states. 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 v N/M = 1/q, q odd.. Within this model the complimentary wavefunction for v=1-1/q is found explicitly, and extremely simple ground state wavefunctions for arbitrary odd-denominator filling factors are proposed.