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 Δ₁ and Δ₂, 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,Δ₁/J₁,Δ₂/J₁) (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|~1/4. These results are relevant for some systems containing CuO chains with edge-sharing CuO₄ units.