Exact solutions and the adiabatic heuristic for quantum Hall states

Martin Greiter, Frank Wilczek

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

An operator formalism is developed for an exactly soluble model of fractional statistics, and used to show that a heuristic principle suggested earlier is rigorously valid in one particular case. For a class of model hamiltonians, Laughlin's Jastrow-type wave functions are obtained explicity from a filled Landau level by smooth extrapolation in quantum statistics. The gap is shown not to close, which allows us to infer the incompressibility of the final states. The analysis is further extended to paired Hall states at even-denominator fillings, which arise adiabatically from an exact but unnormalizable model of superconductivity. Finally, we generalize the model to the torus geometry, and show that theorems restricting the possibilities of quantum statistics on closed surfaces are circumvented in the presence of a magnetic field.

Original languageEnglish (US)
Pages (from-to)577-600
Number of pages24
JournalNuclear Physics, Section B
Volume370
Issue number3
DOIs
StatePublished - Feb 24 1992
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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