Dynamical symmetry enlargement in metallic zigzag carbon nanotubes

We revisit correlation effects in doped metallic zigzag carbon nanotubes by using both the one-loop renormalization group and non-perturbative bosonization techniques. Note that, if a nanotube is placed near a conducting plate, the long-range Coulomb interactions are screened and the resulting short-range interactions can be modelled by on-site and nearest-neighbor repulsive interactions $U$, $V$ and $V_{\perp }$ respectively. Using both analytic and numeric means, we determine the phase diagram of the ground states. For $U\mathrm{/}t<0.5$ ($t$ is the hopping strength), dynamical symmetry enlargement occurs and the low-energy excitations are described by the SO(6) Gross-Neveu model. However, for realistic material parameters $U\mathrm{/}t\sim \mathcal{O}(1)$, the charge sector decouples but there remains an enlarged SO(4) symmetry in the spin sector.