The effect of Landau level (LL) mixing on the $\nu =5∕2$ fractional quantum Hall state is studied directly in a minimal, yet still numerically tractable, approximation. Specifically, the inter-LL excitations with one unit of cyclotron energy are included in the exact diagonalization of a small yet representative number of electrons on a sphere. Significant reduction of the excitation gap found already in this simple model indicates that LL mixing must play an important role in more realistic systems, with a full spectrum of allowed inter-LL excitations. This suggests a possible route to the explanation of the troubling discrepancy between earlier calculations and experiments. On the other hand, even within our limited approach the LL mixing is found to considerably reduce overlaps with the Moore-Read wave function, raising the question of the actual realization of non-Abelian quasiparticles (QPs) at $\nu =5∕2$. In view of the discussed limitations of exact numerics, conclusive resolution of this question will probably require an experiment directly probing the QP statistics.

• Received 28 September 2006

DOI:https://doi.org/10.1103/PhysRevB.74.235319