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Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems

We analyze the localization behavior in a non-Hermitian system subject to a quasiperiodic onsite potential. We characterize localization transitions using multiple quantitative indicators, including inverse participation ratio (IPR), eigenstate fractal dimension (EFD), extended eigenstate ratio (EER), and spectral survival ratio. Despite the breaking of self-dual symmetry due to non-Hermiticity, our results reveal the existence of a critical potential strength, with its value increasing linearly with the nearest-neighbor antisymmetric hopping term. On the other hand, the inclusion of longer-range hopping not only enriches the topological properties but also gives rise to novel localization phenomena. In particular, it induces the emergence of mobility edges, as evidenced by both IPR and EFD, along with distinct features in the spectrum fractal dimension, which we extract using the box-counting method applied to the complex energy spectrum. Additionally, we uncover self-similar structures in various quantities, such as EER and complex eigenvalue ratio, as the potential strength varies. These findings highlight important aspects of localization and fractal phenomena in non-Hermitian quasiperiodic systems.