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.

arXiv commentExposition simplified and shortened. Fermi velocity calculated at 3 more system sizes; parabolic fits improved. Abstract in listing fixed to agree with abstract in paper

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