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

Abstract

The ground state phase diagram of anXXZ chain with asymmetric second-neighbour interactions is studied. We first prove that thismodel 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 andfind that the dependence of the dimer–fluid critical line on the asymmetric interactions ismuch stronger than those of the dimer–Néel critical line and the ferro-fluid first-ordertransition line. In order to understand this result, we analyse eigenvectors ofthe ground state and excitations characterizing each of phases, and show thatonly the doublet excitation can be used to detect the asymmetric interactions.