Superconductivity in a SO(4) symmetric one-dimensional interacting system with diagonal three-body attraction

•We determine phase diagram of a SO(4) symmetric extended Hubbard chain.•The diagonal three-body attraction has an important effect on ground state of the model.•The model considered is of fundamental relevance in the recent ultracold systems.•The study provides an insignificant insight into the superconductivity mechanism.

Stimulated by recent experimental realization of tunability of multi-particle processes in ultracold fermion gases, we study a SO(4) symmetric generalized Hubbard model in an one-dimensional lattice with two-body and three-body interactions up to the nearest neighboring sites. By using the bosonization and renormalization-group schemes, we focus on weak-coupling regime and half-filled band, and determine the ground-state phase diagram, which consists of the Mott-insulator (MI), Luttinger liquid (LL) and Luther-Emery (LE) liquid phases. The diagonal three-body attraction significantly modifies the phase diagram and is responsible for superconducting phases even in the presence of two-body repulsions.