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) J(1) and next-NN J(2) exchange interactions, with anisotropies Delta (1) and Delta (2), 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 (J(2)/J(1), Delta (1)/J(1), Delta (2)/J(1)) (determined by two simple equations) at which the ground state is highly degenerate. M(B) has a jump near this liner and at or near the isotropic case with ferromagnetic J(1) and antiferromagnetic J(2), with \J(2)/J(1)\ similar to 1/4. These results are relevant fur some systems containing CuO chains with edge-sharing CuO4 units.