Ground State Phase Diagram of $\text{SU}(3)$ $t$-$J$ Chain

Distinct from the $\text{SU}(2)$ case, the fermionic systems with $\text{SU}(N)$ symmetry are expected to exhibit novel physics, such as exotic singlet formation. Using the density matrix renormalization group technique, we obtain the ground state phase diagram of the $\text{SU}(3)$ $t$-$J$ chain for density $n<1$. The ground state phase diagram includes the Luttinger liquid, the extended Luther-Emery liquid characterized by a spin gap, and the phase separation state. We quantitatively assess the characteristics of the three phases by measuring spin gap, compressibility, various correlation functions and structure factors. We further study the extended Luther-Emery liquid phase and discover molecular superfluid quasi-long-range order. The mechanism of the molecular superfluid is the combination of three $\text{SU}(3)$ fermions on sites that are not completely connected. Accordingly, we can speculate the behavior of the $\text{SU}(N)$ $t$-$J$ chain model with larger $N$ values, operating within the same filling regime.