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We construct a wavefunction, generalizing the well known Moore-Read Pfaffian,that describes spinless electrons at filling fraction nu=2/5 (or bosons atfilling fraction nu=2/3) as the ground state of a very simple three bodypotential. We find, analogous to the Pfaffian, that when quasiholes are addedthere is a ground state degeneracy which can be identified as zero-modes of thequasiholes. The zero-modes are identified as having semionic statistics. Wewrite this wavefunction as a correlator of the Virasoro minimal model conformalfield theory M(5,3). Since this model is non-unitary, we conclude that thiswavefunction is a quantum critical state. Nonetheless, we find that theoverlaps of this wavefunction with exact diagonalizations in the lowest andfirst excited Landau level are very high, suggesting that this wavefunction mayhave experimental relevance for some transition that may occur in that regime.Comment: 13 pages, 2 figure

physical review. b, condensed matter and materials physics

Construction of a paired wave function for spinless electrons at filling fraction<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>∕</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:math>

Construction of a paired wave function for spinless electrons at filling fractionν=2∕5