Ground-state phase diagram of the one-dimensional 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) natures, 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, which results larger than the variational but smaller than the RG one. Furthermore, we show that the spin gap can reach a sizable value (similar to 0.1t) 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.