Extended cluster spin-1/2 XXZ chain

We study the quantum phase transitions in the extended cluster spin-1/2 XXZ chain, which is equivalent to a 1D spin-1/2 XXZ model with three-spin interaction. The ground state phase diagram of the 1D spin-1/2 anisotropic XXZ model is known. Depending on the value of the anisotropy parameter, the ground state exhibits the ordering of the Luttinger liquid (LL), the Neel and the saturated ferromagnetic phases. In the absence of the anisotropy, it was shown that the three-spin interaction induces a quantum phase transition between two kinds of the LL phases. In the presence of the anisotropy, by using the analytical and numerical methods, the extended ground state phase diagram of the model is obtained.