Exact Zero Temperature Correlation Functions for Two-Leg Hubbard Ladders and Carbon Nanotubes

Abstract

Motivated by recent work of Lin, Balents, and Fisher (cond-mat/9801285), we compute correlation functions at zero temperature for weakly coupled two-leg Hubbard ladders and (N,N) armchair carbon nanotubes. Lin et al. argued that such systems renormalize towards the SO(8) Gross-Neveu model, an integrable theory. We exploit this integrability to perform the computation at the SO(8) invariant point. Terms breaking this symmetry can be treated systematically in perturbation theory, leading to a model with the same qualitative features. Using said correlators, we determine the optical conductivity, the single particle spectral function, and the I-V curve for tunneling into the system from an external lead. The frequency, ω, dependent optical conductivity is determined exactly for ω< 3m (m being the fermion particle mass in the SO(8) Gross-Neveu model). It is characterized by a sharp ``exciton'' peak followed by the onset of the particle-hole continuum. Similarly, we obtain the exact single particle spectral function for energies less than 3m. The latter possesses a delta function peak arising from single particle excitations, together with a two particle continuum. The final quantity we compute is the tunneling I-V curve to lowest non-vanishing order in the tunneling matrix elements. For this quantity, we present exact results for voltages, V < (1+\sqrt(3))m. The resulting differential conductance is marked by a finite jump at the energy of the onset of tunneling into the continuum of two particle states. All calculations are done through form-factor expansions of correlation functions. Finite truncations of such expansions give exact closed form expressions below given energy thresholds. To facilitate these calculations, we compute a number of previously unknown one and two particle form factors.