In this manuscript, we study a non-Hermitian spin-1/2 XY system with two sites in the presence of an alternating, imaginary and transverse magnetic field. The eigenvalues and eigenstates of the Hamiltonian are exactly solved. In addition, the energy spectrum of the system is discussed and an exceptional point is obtained which distinguishes the parity-time reversal (PT ) symmetry and symmetry broken phases. Then we study the ground-state phase diagram which is illustrated by a unit sphere with the anisotropic parameter γ, reduced real and imaginary magnetic fields (h 0 and η 0 ) as variables, and find that there are two possible ground states. We further discuss the ground-state concurrence and find that it is only related to γ and h 0 when the value ranges of the parameters are outside the sphere. Moreover, it only depends on η 0 and is always the maximum when parameters are inside the sphere. When ground states are degenerate, the entanglement of the pure state which consists of two ground states is greater than that of the mixed state. We also study the thermal entanglement and find that concurrence suddenly changes with temperature and the reduced external magnetic fields (h 0 and η 0 ). Especially, the change fades away with increasing γ.Furthermore, when temperature approaches zero, there are overlapping parts between the thermal and non-degenerate ground-state entanglements and it is indicated that the thermal entanglement is realized by non-degenerate ground states.
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