Origin of the ν=2/5 fractional quantum Hall effect

We present numerical evidence in support of the view that the physical origin of the fractional quantum Hall effect at ν=n/(2n+1) is associated with the fact that this is the largest filling factor at which an n-component system of electrons can avoid having any pair of electrons occur in a state of relative angular momentum 1. Our calculations, for n=2, are based on a model in which the Hilbert space is truncated to the two lowest Landau levels and the Landau-level separation, ħ${\mathrm{\omega }}_{\mathit{c}}$, is a parameter of the model. For ħ${\mathrm{\omega }}_{\mathit{c}}$=0 and short-range repulsive interactions, a zero-energy incompressible ground state occurs at ν=2/5. Our numerical results suggest that, in agreement with arguments advanced by J. K. Jain, this incompressibility survives to the strong-field limit ħ${\mathrm{\omega }}_{\mathit{c}}$=∞.