The ground state of an XXZ chain with asymmetric second-neighbour interactions

The ground state phase diagram of an XXZ chain with asymmetric second-neighbour interactions is studied. We first prove that this model has the doubly degenerate exact dimer ground state under some conditions. Then, by using the level spectroscopy method, we calculate the ground state phase diagram and find that the dependence of the dimer-fluid critical line on the asymmetric interactions is much stronger than those of the dimer-Neel critical line and the ferro-fluid first-order transition line. In order to understand this result, we analyse eigenvectors of the ground state and excitations characterizing each of phases, and show that only the doublet excitation can be used to detect the asymmetric interactions