Effective interaction in bosonic systems of quasiparticles in the fractional quantum Hall effect
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The spectra of strongly interacting bosons for small quantum Hall systems on the sphere are calculated numerically. The essential features, which are already known for fermions around the filling factorv=1/3 reappear for bosons around the filling factorv=1/2. Haldane's wavefunctions, which describe one quasiparticle at filling factorv=1/3, are generalized to yield model wavefunctions for the angular momentum eigenstates of two quasiparticles. For two quasiholes, these model wavefunctions are used to calculate potential coefficients of the quasihole interaction. Within the hierarchy model, this allows a rough quantitative description of the low-lying levels at filling factorv=2/7 of the fermionic system. The thermodynamic limit for the first two potential coefficients is performed, showing that the quasihole interaction keeps its strong short range part in the bulk limit.
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