The energy gaps for the fractional quantum Hall effect at filling fractions 1/3, 1/5, and 1/7 have been calculated by variational Monte Carlo using Jain's composite-fermion wave functions. Results have been obtained before and after projection onto the lowest Landau level. The projected energy gaps agree well with exact-diagonalization results for small systems, lending support to the composite-fermion theory.

arXiv:cond-mat/9406110Physical review. B, Condensed matterApr 15, 199518 citations

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

Parsa Bonderson, Adrian E. Feiguin, Chetan Nayak

arXiv:1008.4173Physical Review LettersMay 5, 201139 citations

arXiv:cond-mat/9401066 · Physical review. B, Condensed matter

Ground-state energy and quasiparticle gaps in ν=N/(2N±1) fractional-quantum-Hall-effect states

Dmitri V. Khveshchenko

Published Apr 15, 1994• 2 citations

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Abstract

{\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\eta}}}

is found to be greater than 1 and to depend nontrivially on the interaction potential. The dependence of quasiparticle gaps agrees with the results of recent measurements by R. R. Du et al.

DOI: 10.1103/physrevb.49.10514

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We present the first numerical computation of the neutral fermion gap, ${\ensuremath{\Delta}}_{F}$, in the $\ensuremath{\nu}=5/2$ quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find ${\ensuremath{\Delta}}_{F}\ensuremath{\approx}0.027\frac{{e}^{2}}{\ensuremath{\epsilon}{\ensuremath{\ell}}_{0}}$, comparable to the charge gap. 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 ${\ensuremath{\xi}}_{F}={v}_{F}/{\ensuremath{\Delta}}_{F}\ensuremath{\approx}1.3{\ensuremath{\ell}}_{0}$. We comment on implications for experiments, topological quantum information processing, and electronic mechanisms of superconductivity.We present the first numerical computation of the neutral fermion gap, ${\ensuremath{\Delta}}_{F}$, in the $\ensuremath{\nu}=5/2$ quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find ${\ensuremath{\Delta}}_{F}\ensuremath{\approx}0.027\frac{{e}^{2}}{\ensuremath{\epsilon}{\ensuremath{\ell}}_{0}}$, comparable to the charge gap. 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 ${\ensuremath{\xi}}_{F}={v}_{F}/{\ensuremath{\Delta}}_{F}\ensuremath{\approx}1.3{\ensuremath{\ell}}_{0}$. We comment on implications for experiments, topological quantum information processing, and electronic mechanisms of superconductivity.

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{\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\eta}}}

is found to be greater than 1 and to depend nontrivially on the interaction potential. The dependence of quasiparticle gaps agrees with the results of recent measurements by R. R. Du et al.

{v}_{F}

for neutral fermions from the low-energy spectra for odd numbers of electrons, and thereby obtain a correlation length ${\ensuremath{\xi}}_{F}={v}_{F}/{\ensuremath{\Delta}}_{F}\ensuremath{\approx}1.3{\ensuremath{\ell}}_{0}$. We comment on implications for experiments, topological quantum information processing, and electronic mechanisms of superconductivity.