Magnetization process of the spin-12XXZmodels on square and cubic lattices

The magnetization process of the spin-1/2 antiferromagnetic $\mathrm{XXZ}$ models with Ising-like anisotropy in the ground state is investigated. We show numerically that the Ising-like $\mathrm{XXZ}$ models on square and cubic lattices show a first-order phase transition at some critical magnetic field. We estimate the value of the critical field and the magnetization jump on the basis of the Maxwell construction. The magnetization jump in the Ising limit is investigated by means of perturbation theory. Based on our numerical results, we briefly discuss the phase diagram of the extended Bose-Hubbard model in the hard-core limit.