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Ground-State Phase Diagram of the 1D t-J model

We examine the ground-state phase diagram of the t-J model in one dimension by means of the Density Matrix Renormalization Group. This model is characterized by a rich phase diagram as a function of the exchange interaction J and the density n, displaying Luttinger-liquid (LL) behavior both of repulsive and attractive (i.e. superconducting) nature, a spin-gap phase, and phase-separation. The phase boundaries separating the repulsive from the attractive LL phase as J is increased, and also the boundaries of the spin-gap region at low densities, and phase-separation at even larger J, are determined on the basis of correlation functions and energy-gaps. In particular, we shed light on a contradiction between variational and renormalization-group (RG) results about the extent of the spin-gap phase, that results larger than the variational but smaller than the RG one. Furthermore, we show that the spin gap can reach a sizable value (~ 0.1 t) at low enough filling, such that preformed pairs should be observable at temperatures below these energy scales. No evidence for a phase with clustering of more than two particles is found on approaching phase separation.