Interaction induced dimerization in zigzag single wall carbon nanotubes

We derive a low-energy effective model of metallic zigzag carbon nanotubes at half filling. We show that there are three important features characterizing the low-energy properties of these systems: the long-range Coulomb interaction, umklapp scattering and an explicit dimerization generated by interactions. The ratio of the dimerization induced gap and the Mott gap induced by the umklapp interactions is dependent on the radius of the nanotube and can drive the system through a quantum phase transition with SU(2)_1 quantum symmetry. We consider the physical properties of the phases on either side of this transition which should be relevant for realistic nanotubes.