Composite fermions in the Hilbert space of the lowest electronic Landau level

J. K. Jain, R. K. Kamilla

Research output: Contribution to journalArticle

157 Citations (Scopus)

Abstract

Single particle basis functions for composite fermions are obtained from which manycomposite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ∼ 0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.

Original languageEnglish (US)
Pages (from-to)2621-2660
Number of pages40
JournalInternational Journal of Modern Physics B
Volume11
Issue number22
DOIs
StatePublished - Sep 10 1997

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Hilbert space
fermions
composite materials
electronics
quantum Hall effect
ground state
determinants
excitons
wave functions
excitation

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

Cite this

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abstract = "Single particle basis functions for composite fermions are obtained from which manycomposite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ∼ 0.1{\%} and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.",
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Composite fermions in the Hilbert space of the lowest electronic Landau level. / Jain, J. K.; Kamilla, R. K.

In: International Journal of Modern Physics B, Vol. 11, No. 22, 10.09.1997, p. 2621-2660.

Research output: Contribution to journalArticle

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