  In this manuscript, we study the non-Hermitian spin-1/2 XY model in the
presence of the alternating, imaginary and transverse magnetic fields. For the
two-site spin system, we solve exactly the energy spectrum and phase diagram,
also calculate the ground-state and thermal entanglements by using the concept
of the concurrence. It is found that the two-site concurrence in the eigenstate
which only depends on the imaginary magnetic field {\eta} is always equal to
one in the region of PT symmetry, while it decreases with {\eta} in the
PT-symmetric broken region. Especially, the concurrence shows the non-analytic
behavior at the exceptional point, and the same is true in the case of the
biorthogonal basis, which indicates that the concurrence can characterize the
phase transition in this non-Hermitian system. The interesting thing is that
{\eta} weakens the thermal entanglement when the system is isotropic and
enhances the entanglement when the system becomes the Ising model. For the
one-dimensional spin chain, the magnetization and entanglement are further
studied by using the two-spin cluster mean-field approximation. The results
show that their variations have opposite trends with the magnetic fields.
Moreover, the system exists the first-order quantum phase transitions for some
anisotropic parameters in the PT-symmetry region, and the entanglement changes
suddenly at the quantum phase transition point.
