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Electron-Hole Correlation in Fractional Quantum Hall Systems

The 2D system of electron confined to the lowest Landau level is described using a representation of the density matrix depending both on electron and hole coordinates. Condensation of the electron system into a fractional quantum Hall state is associated to clustering of particle and hole coordinates. The correlation of particle and hole coordinates is studied and groundstate wave functions are derived for $ν=p/(2p \pm 1)$. These wave functions prove to be accurate for the studied cases $ν=2/3$ and $3/5$ and are identical to pair wave functions [R. Morf et al., Phys. Rev. B34, 3037 (1986)] for $ν=2/3$ and $2/5$.