Two-Leg Ladders and Carbon Nanotubes: Exact Properties at Finite Doping

TL;DR

This paper uses exact solutions to analyze doped two-leg Hubbard ladders and armchair carbon nanotubes, revealing persistent gaps and near free-fermion behavior, with implications for high-temperature superconductivity theories.

Contribution

It provides exact calculations of spin and particle gaps and Luttinger parameters in doped systems using thermodynamic Bethe ansatz, extending understanding of their low-energy properties.

Findings

Spin and particle gaps remain finite at finite doping.

Luttinger parameter stays close to 1, indicating near free-fermion behavior.

Presence of the $$-resonance linked to high-$T_c$ superconductivity theories.

Abstract

Recently Lin, Balents, and Fisher have demonstrated that two-leg Hubbard ladders and armchair carbon nanotubes renormalize onto the integrable SO(8) Gross-Neveu model. We exploit this integrability to examine these systems in their doped phase. Using thermodynamic Bethe ansatz, we compute exactly both the spin and single particle gaps and the Luttinger parameter describing low energy excitations. We show both the spin and particle gap do not vanish at finite doping, while the Luttinger parameter remains close to its free fermionic value of 1. A similar set of conclusions is drawn for the undoped systems' behaviour in a finite magnetic field. We also comment on the exisitence in these systems of the $\pi$-resonance, a hallmark of Zhang's SO(5) theory of high $T_c$ superconductivity.