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.