Phase diagram of the one-dimensional t-J model with long-range dipolar interactions

We study systematically the effect of long-range dipolar interactions on the ground-state phase diagram of the one-dimensional $t\text{-}J$ model by means of the density matrix renormalization group. While the basic phases described by the Luttinger parameter $K_\rho$ , namely, the repulsive Luttinger liquid (metallic phase, $K_\rho 1$ ), and the phase separation $(K_\rho \rightarrow \infty)$ , are similar to those of the conventional $t\text{-}J$ model, the presence of the long-range dipolar interactions leads to significant differences. i) At high-density regime, the phase boundaries of these three phases are even pushed to the large-J region; ii) at low-density regime, these phase boundaries shift toward the small-J region and, most importantly, iii) the spin-gap region spreads across the boundary of $K_\rho = 1$ , suggesting an exotic metallic phase with spin-gap, which is absent in the conventional $t\text{-}J$ model. The result indicates that the long-range dipolar interactions have a significant influence on the ground-state properties of the one-dimensional $t\text{-}J$ model. Its implication on the pseudogap phenomenon of the hole-doped cuprates is briefly discussed