Phase transition in the fractional quantum Hall effect

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Abstract
We present a systematic study, both analytical and numerical, of the Hall Hamiltonian (including the Hall electric field) as function of the distance between neighboring Landau orbitals. We find a series of high-symmetry states, which consist of a periodic array of electron drops, that act as generators of the ground state. We also find a series of phase transitions in which the size of the dominant electron drop increases when the distance between adjacent orbitals is decreased. Difference between odd- and even-denominator filling factors become apparent. A scaling length of the problem is also found.