Numerical Calculation of the Neutral Fermion Gap at $ν=5/2$

We present the first numerical computation of the neutral fermion gap, $Δ_ψ$, in the $ν=5/2$ quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find $Δ_ψ\approx 0.027 \frac{e^2}{ε\ell_0}$, comparable to the charge gap, and discuss the implications for topological quantum information processing. We also deduce an effective Fermi velocity $v_F$ for neutral fermions from the low-energy spectra for odd numbers of electrons, and thereby obtain a correlation length $ξ_ψ={v_F}/Δ_ψ \approx 1.3\, \ell_0$. We comment on the implications of our results for electronic mechanisms of superconductivity more generally.

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