  By means of the recently proposed algorithm based on the tensor product
states, the magnetization process of the spin-1/2 anti-ferromagnetic XXZ model
on a square lattice is investigated. In the large spin-anisotropy limit, clear
evidence of a first-order spin-flip transition is observed as an external
magnetic field is increased. Our findings of the critical field and the
discrete jumps in various local order parameters are in good agreement with the
quantum Monte Carlo data in the literature. Our results imply that this
algorithm can be an accurate and efficient numerical approach in studying
first-order quantum phase transitions in two dimensions.
