Two-leg ladders and carbon nanotubes: Exact properties at finite doping

Abstract

Recently Lin, Balents, and Fisher have demonstrated that two-leg Hubbard ladders and armchair carbon nanotubes renormalize towards the integrable SO(8) Gross-Neveu model. Here, we exploit this integrability to extract non-trivial effects of interactions in these systems in their doped phase. We so obtain results that could not be expected a priori. Using thermodynamic Bethe ansatz, we compute exactly both the spin and single-particle gaps and the Luttinger parameter describing low-energy excitations. We show rigourously both the spin gap and the electron gap do not vanish at finite doping, while the Luttinger parameter remains close to its free Fermionic value of 1, even for larger values of doping. A similar set of conclusions is drawn for the undoped systems' behavior in a finite magnetic field. We also comment on the existence in these systems of the $\ensuremath{\pi}$ resonance, a hallmark of Zhang's SO(5) theory of high-${T}_{c}$ superconductivity.