Title:
Coulomb interaction, umklapp scaterring and quantum criticality in zig-zag nanotubes

Abstract:
We derive a low energy effective model of metallic zig-zag carbon nanotubes at half filling. We show that there are three important features to consider: the long range Coulomb interaction, the Umklapp scattering and an explicit dimerization in the interactions generating single particle band gaps. 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. We consider the physical properties of the phases either side of this transition which should be relevant for realistic nanotubes