Phase Diagram of the 1D t-J Model

We study the ground state properties of the one-dimensional t-J model using the Density Matrix Renormalization Group (DMRG), obtaining its phase diagram. By measuring the energy and correlations functions we have identified four different phases: metal, spin-gap with singlet superconductivity, superconductivity without spin-gap, and phase separation. We found at low densities that the phase separation region is shifted to higher values of J/t in comparison to previous results [1-3]. We confirmed also the results of M. Nakamura et al. [4], who claim, in contrast to other studies [2-3], that a spin gap region is present at densities higher than 0.25.We show that on going from the Luttinger Liquid to the spin-gap phase, electrons form pairs visible in real space. We also discarded the existence of a four bound electron phase by observing the density in real space.