Magnetization jump in the XXZ chain with next-nearest-neighbor exchange

We study the dependence of the magnetization M with magnetic field B at zero temperature in the spin-1/2 XXZ chain with nearest-neighbor (NN) J1 and next-NN J2 exchange interactions, with anisotropies Delta1 and Delta2 respectively. The region of parameters for which a jump in M(B) exists is studied using numerical diagonalization, and analytical results for two magnons on a ferromagnetic background in the thermodynamic limit. We find a line in the parameter space (J2/J1, Delta1/J1, Delta2/J2) (determined by two simple equations) at which the ground state is highly degenerate. M(B) has a jump near this line, and at or near the isotropic case with ferromagnetic J1 and antiferromagnetic J2, with |J2/J1| near 1/4. These results are relevant for some systems containing CuO chains with edge-sharing CuO4 units.