Non-Hermitian Stark many-body localization

Utilizing exact diagonalization techniques, we investigate a one-dimensional, nonreciprocal, interacting hard-core boson model under a Stark potential with tail curvature. By employing the nonzero 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 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.