  Recently Lin, Balents, and Fisher have demonstrated that two-leg Hubbard
ladders and armchair carbon nanotubes renormalize onto the integrable SO(8)
Gross-Neveu model. We exploit this integrability to examine these systems in
their doped phase. Using thermodynamic Bethe ansatz, we compute exactly both
the spin and single particle gaps and the Luttinger parameter describing low
energy excitations. We show both the spin and particle gap do not vanish at
finite doping, while the Luttinger parameter remains close to its free
fermionic value of 1. A similar set of conclusions is drawn for the undoped
systems' behaviour in a finite magnetic field. We also comment on the
exisitence in these systems of the $\pi$-resonance, a hallmark of Zhang's SO(5)
theory of high $T_c$ superconductivity.
