  Utilizing exact diagonalization (ED) techniques, we investigate a
one-dimensional, non-reciprocal, interacting hard-core boson model under a
Stark potential with tail curvature. By employing the non-zero imaginary
eigenenergies ratio, half-chain entanglement entropy, and eigenstate
instability, we numerically confirm that the critical points of spectral
real-complex (RC) transition and many-body localization (MBL) phase transition
are not identical, and an examination of the phase diagrams reveals that the
spectral RC transition arises before the MBL phase transition, which suggests
the existence of a novel non-MBL-driven spectral RC transition. These findings
are quite unexpected, and they are entirely different from observations in
disorder-driven interacting non-Hermitian systems. This work provides a useful
reference for further research on phase transitions in disorder-free
interacting non-Hermitian systems.
