Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping

In the last few years, several works have identified the concurrence of the spectral, delocalization-localization and topological phase transitions in non-Hermitian quasiperiodic systems in the presence of time-reversal symmetry (TRS), with or without interaction. In this work, we investigate one-dimensional interacting non-Hermitian quasiperiodic lattices with asymmetric power-law hopping and unveil that although the Hamiltonian respects the TRS, the reality of the eigenspectrum does not necessarily indicate a topologically trivial non-Hermitian many-body localization (NHMBL) regime. In fact, we reveal the emergence of a topologically trivial intermediate regime, where the states that are primarily multifractal in nature can also possess a fully real spectrum, thereby restoring the TRS before crossing over to the NHMBL phase. Moreover, in the entire intermediate regime, the interaction completely destroys the multifractal and mobility edges observed in the non-interacting counterpart. Besides, we unveil that due to the long-range nature of the hopping, the entire topologically non-trivial ergodic regime under the periodic boundary condition does not always give rise to boundary localized skin modes under the open boundary condition. Our findings thus advances and deepens the understanding about the emergence of non-trivial phases due to the interplay of interaction and long-range hopping in non-Hermitian quasiperiodic systems.