Deformed Hubbard operator, bosonization, and phase diagram of the one-dimensionalt−Jmodel

Abstract

We present an analytic study of the phase diagram of the one-dimensional $t\ensuremath{-}J$ 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 $\ensuremath{\Delta}$ 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 $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}1,$ 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.