Correlation gap in armchair carbon nanotubes

We revisit the problem of the correlation gap in (n,n) armchair carbon nanotubes, that would be metallic in the absence of electron-electron correlations. We attack the problem in the context of a Hubbard model with on-site repulsion U only, and we show that the scaling of the gap as exp(-nt/U) predicted by Balents and Fisher (Phys. Rev. B 55, R11973 (1997)), can only be valid if U is not too large, even for very large values of n. Using Hartree--Fock calculations and Renormalisation Group arguments we derive the scaling of the gap as a function of n for a given value of U. Possible applications for the magnitude of the correlation gap in armchair carbon nanotubes will be discussed.