Phase diagram of the XXZ chain with next-nearest-neighbor interactions

We calculate the quantum phase diagram of the XXZ chain with nearestneighbor (NN) J1 and next-NN exchange J2 with anisotropies ∆1 and ∆2 respectively. In particular we consider the case ∆1 = −∆2 to interpolate between the XX chain (∆i = 0) and the isotropic model with ferromagnetic J2. For ∆1 < −1, a ferromagnetic and two antiferromagnetic phases exist. For |∆i| < 1, the boundary between the dimer and spin fluid phases is determined by the method of crossing of excitation spectra. For large J2/J1, this method seems to indicate the existence of a second spin fluid critical phase. However, an analysis of the spin stiffness and magnetic susceptibility for ∆1 = ∆2 = 1 suggest that a small gap is present. Typeset using REVTEX 1