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In this work, the interplay among non-Hermiticity, quasidisorder, andrepulsive interaction is studied for hard-core bosons confined in aone-dimensional optical lattice, where the non-Hermiticity is induced by thenon-reciprocal hoppings and the on-site gain and loss breaking thetime-reversal symmetry. The energy spectra of the system are fully complex andthe time evolution of the real part of the energy is dynamically stable. Bymeans of the entanglement entropy and its dynamical evolution, as well as theinverse participation ratio, the many-body localization (MBL) is found inplaying a key role on the stability of the dynamical behavior. Meanwhile, thenearest-neighbor level spacings statistics shows the MBL transition accompaniedby the transition from the Ginibre distribution to the complex Poissondistribution, different from the one in the time-reversal invariant system.Moreover, the dynamical stability of the real part of the energy and the MBLtransition can be characterized by the winding number. By the scaling exponentof the entanglement entropy, it is argued that the MBL transition in thecomplex energy spectrum system shall belong to a new university class.

Stable real-energy spectral dynamics with topological transitions and non-Hermitian many-body localization