Off-diagonal long-range order in Laughlin’s states for particles obeying fractional statistics

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Abstract
Laughlin has proposed mean-field wave functions for particles obeying (1-1/J) fractional statistics where J is an integer. We demonstrate off-diagonal long-range order in these wave functions, which is closely related to the off-diagonal long-range order in the electronic wave functions corresponding to J completely filled Landau levels. The presence of off-diagonal long-range order signifies Bose condensation of bosonlike multiplets containing J particles. For J=2, which may be relevant to high-temperature superconductivity, our result implies Cooper pairing in Laughlin’s wave function for half-fermions.