Phase diagram of the one-dimensional t-J model.

We present an analytic study of the phase diagram of the one-dimensional t − J model and a couple of its cousins. To deal with the interactions induced by the no double occupancy constraints, we introduce a deformation of the Hubbard operators. When the deformation parameter ∆ is small, the induced interactions are softened, accessible by perturbation theory. We combine bososnization with renormalization group techniques to map out the phase diagram of the system. We argue that when ∆ → 1, there is no essential change in the phase diagram. Comparison with the existing results in the literature obtained by other methods justifies our deformation approach.