Luther-Emery liquid and dominant singlet superconductivity in the two-orbital Hubbard chain

We investigate the pairing tendencies in the two-orbital Hubbard chain at intermediate repulsive interaction strengths $U$, and for degenerate orbitals. At half-filling and large $U$, the ferromagnetic Hund's coupling, $J_\mathrm{H}$, generates effective spin-$1$ moments, with antiferromagnetic correlations between sites. Thus the system can be viewed as an electronic generalization of Haldane's spin-$1$ chain in that limit. Using large-scale density matrix renormalization group calculations, we study the system's behavior under light hole-doping. For $U=1.6$ in units of the non-interacting bandwidth and $J_\mathrm{H}/U\gtrsim 0.275$ we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, similarly to the behavior of doped one-orbital two-leg ladders at weak coupling. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity. Candidate materials to realize this physics are discussed.