Quantum Hall effect of interacting electrons in a periodic potential

@article{Pfannkuche1997QuantumHE,
  title={Quantum Hall effect of interacting electrons in a periodic potential},
  author={Daniela Pfannkuche and Allan H. MacDonald Department of Physics and Indiana University and Bloomington and Usa and Max-Planck-Institut fuer Festkoerperforschung and Stuttgart and H Germany},
  journal={Physical Review B},
  year={1997},
  volume={56}
}
We consider the influence of an external periodic potential on the fractional quantum Hall effect. For many electrons on a torus, we find that at finite system sizeL the splitting of incompressible ground-state degeneracies by a weak external potential is proportional to exp(2L/j). We present numerical results consistent with a scenario in which j diverges at a continuous phase transition from fractional to integer quantum Hall states which occurs at a critical periodic potential strength… 
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