关键词: disordered non-Hermitian systems, mosaic structure, mobility edge

Abstract: We focus on a modified version of the non-Hermitian Aubry-Andre-Harper (AAH) model, which has garnered significant attention due to its ability to investigate localization phenomena, metal-insulator transitions, and topological phase transitions. We have made two key modifications to the non-Hermitian AAH model: First, we introduce a mosaic structure that allows for the mixing of localized and extended states, resulting in the appearance of mobility edges, which is a feature that is not present in the original non-Hermitian AAH model. In the insulating phase, leveraging Fields Medal winner Avila's global theory, our work derives a theoretical description of the localization length, a crucial parameter previously unavailable in the non-Hermitian AAH model, and obtains the exact expression for mobility edges. We studied the variation of the energy spectrum with the amplitude and quantitatively determined the topological phase transition point within the spectrum. Furthermore, we introduced an asymmetric parameter $g$ and calculated its corresponding localization length, the location of mobility edges, as well as the precise expressions for its extended and localized states. By quantitatively calculating the Lyapunov exponent of dual models, our work reveals an interesting fact about the robustness of localized states: within an appropriate relationship between $g$ and the coupling potential strength, the localized states exhibit similar characteristics to those in the mosaic non-Hermitian AAH model. Our work offers a more complete and nuanced understanding of localization phenomena in disordered non-Hermitian systems, paving the way for further research in this promising field.

Key words: disordered non-Hermitian systems, mosaic structure, mobility edge