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.

Exposition 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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Cited by in corpus (13)

• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid
• Josephson Coupled Moore-Read States
• Topological blockade and measurement of topological charge
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Dipolar bogolons: from superfluids to Pfaffians
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• Critical Majorana fermion at a topological quantum Hall bilayer transition