Quantum Phase Diagram of thet−JzChain Model

We present the quantum phase diagram of the one-dimensional $t$- $J_z$ model for arbitrary spin (integer or half-integer) and sign of the spin-spin interaction $J_z$, using an exact mapping to a spinless fermion model that can be solved exactly using the Bethe ansatz. We discuss its superconducting phase as a function of hole doping $\nu$. Motivated by the new paradigm of high temperature superconductivity, the stripe phase, we also consider the effect the antiferromagnetic background has on the $t$- $J_z$ chain intended to mimic the stripe segments.