The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime

We compute the effect of Landau-level-mixing on the effective two-body and three-body pseudopotentials for electrons in the lowest and second Landau levels. We find that the resulting effective three-body interaction is attractive in the lowest relative angular momentum channel. The renormalization of the two-body pseudopotentials also shows interesting structure. We comment on the implications for the $\nu =5\mathrm{/}2$ fractional quantum Hall state.