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

Abstract

We present the first numerical computation of the neutral fermion gap, $\Delta_\psi$, 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 $\Delta_\psi \approx 0.027 \frac{e^2}{\epsilon \ell_0}$, 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 $\xi_{\psi}={v_F}/\Delta_{\psi} \approx 1.3\, \ell_0$. We comment on the implications of our results for electronic mechanisms of superconductivity more generally.