Numerical Calculation of the Neutral Fermion Gap at the ν=5/2 Fractional Quantum Hall State

We present the first numerical computation of the neutral fermion gap, Delta(F), in the nu = 5/2 quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find Delta(F) approximate to 0: 027 e(2)/el(0), comparable to the charge gap. We also deduce an effective Fermi velocity nu F for neutral fermions from the low-energy spectra for odd numbers of electrons, and thereby obtain a correlation length zeta(F) = nu(F)/Delta(F) approximate to 1.3l(0). We comment on implications for experiments, topological quantum information processing, and electronic mechanisms of superconductivity.