  We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain.
To allow for doping, we extend the original spin chain Hamiltonian into a
fermionic model involving a two-orbital Hubbard chain at intermediate or strong
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. Using large-scale density matrix renormalization group
calculations, we study accurately the system's behavior under light
hole-doping. For $U=1.6$ in units of the non-interacting bandwidth and for
$J_\mathrm{H}/U\gtrsim 0.275$ we find that singlet pairing dominates the
long-distance physics, establishing this system as a promising platform for
repulsively mediated superconductivity. We provide concrete examples of
materials that could realize the physics described here. We also provide
evidence that the system approaches a Luther-Emery liquid state at large system
sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak
coupling, which also have superconducting tendencies. 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.
