  We show how lattice Quantum Monte Carlo can be applied to the electronic
properties of carbon nanotubes in the presence of strong electron-electron
correlations. We employ the path-integral formalism and use methods developed
within the lattice QCD community for our numerical work. Our lattice
Hamiltonian is closely related to the hexagonal Hubbard model augmented by a
long-range electron-electron interaction. We apply our method to the
single-quasiparticle spectrum of the (3,3) armchair nanotube configuration, and
consider the effects of strong electron-electron correlations. Our approach is
equally applicable to other nanotubes, as well as to other carbon
nanostructures. We benchmark our Monte Carlo calculations against the two- and
four-site Hubbard models, where a direct numerical solution is feasible.
