  In the traditional quantum theory, one-dimensional quantum spin models
possess a factorization surface where the ground states are fully separable
having vanishing bipartite as well as multipartite entanglement. We report that
in the non-Hermitian counterpart of these models, these factorization surfaces
either can predict the exceptional points where the unbroken-to-broken
transition occurs or can guarantee the reality of the spectrum, thereby
proposing a procedure to reveal the unbroken phase. We first analytically
demonstrate it for the nearest-neighbour rotation-time RT-symmetric XY model
with uniform and alternating transverse magnetic fields, referred to as the
iATXY model. Exact diagonalization techniques are then employed to establish
this fact for the RT-symmetric XYZ model with short- and long-range
interactions as well as for the long-ranged iATXY model. Moreover, we show that
although the factorization surface prescribes the unbroken phase of the
non-Hermitian model, the bipartite nearest-neighbour entanglement at the
exceptional point is nonvanishing.
