Correlation effects of single-wall carbon nanotubes in weak coupling

Single-wall carbon nanotubes with on-site interaction U much less than t an studied by a controlled renormalization group method. When formulated as a system of Ni flavors of interacting Dirac fermions, the effective model at generic filling resembles a set of quasi-1D Hubbard chains. For the undoped (N-y,N-y) armchair and the (N-x,-N-x) zigzag with N-x = 3n, specific mappings to the two-chain Hubbard model at half filling with effective interaction u(eff)=U/Ny and 2U/N-x are found from this more general equivalence. The phase diagrams of the (3,3) armchair and the (6,-6) zigzag at generic fillings are studied and compared as an example.