Deformed Hubbard operator, bosonization, and 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 bosonization 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. A comparison with the existing results in the literature obtained by other methods justifies our deformation approach.