  We investigate the phase diagram of an anisotropic ferrimagnet spin-(1/2, 1)
in the presence of a non-commuting (transverse) magnetic field. We find a
magnetization plateau for the isotropic case while there is no plateau for the
anisotropic ferrimagnet. The magnetization plateau can appear only when the
Hamiltonian has the U(1) symmetry in the presence of the magnetic field. The
anisotropic model is driven by the magnetic field from the N\'{e}el phase for
low fields to the spin-flop phase for intermediate fields and then to the
paramagnetic phase for high fields. We find the quantum critical points and
their dependence on the anisotropy of the aforementioned field-induced quantum
phase transitions. The spin-flop phase corresponds to the spontaneous breaking
of Z2 symmetry. We use the numerical density matrix renormalization group and
analytic spin wave theory to find the phase diagram of the model. The energy
gap, sublattice magnetization, and total magnetization parallel and
perpendicular to the magnetic field are also calculated. The elementary
excitation spectrums of the model are obtained via the spin wave theory in the
three different regimes depending on the strength of the magnetic field.
