Phase diagram of the one-dimensional t1−t2−J model: Ferromagnetism, triplet pairing, and charge and pair density waves

We present a density matrix renormalization group study of an extended t-J model with hopping to the first and second neighbors---the one-dimensional t₁-t₂-J model. The full phase diagram as a function of the density n and exchange strength J, for both positive and negative values of t₂, is obtained. For t₂=-0.5 we observe that, in the strongly interacting region, Nagaoka ferromagnetism is accompanied by a triplet pair density wave (PDW) upon doping. As the spin exchange J increases, a charge density wave phase emerges and then gives way to singlet superconductivity (SC). This phase behaves as a singlet PDW with vanishing spacial average of the order parameter and a spin gap. When t₂=0.5, the physics is basically reminiscent of the conventional t-J model, undergoing a transition from a metallic to a SC phase as a function of J.