The key concept of mobility edge, which marks the critical transition between extended and localized states in the energy domain, has attracted significant interest in the cutting-edge frontiers of modern physics due to its profound implications for understanding localization and transport properties in disordered systems. However, a generic way to construct multiple mobility edges (MME) is still ambiguous and lacking. In this work, we propose a brief scheme to engineer both real and complex exact multiple mobility edges exploiting a few coupled one-dimensional quasiperiodic chains. We study the extended-localized transitions of coupled one-dimensional quasiperiodic chains along the chain direction. The model combines both the well-established quasiperiodicity and a kind of freshly introduced staggered nonreciprocity, which are aligned in two mutually perpendicular directions, within a unified framework. Based on analytical analysis, we predict that when the couplings between quasiperiodic chains are weak, the system will be in a mixed phase in which the localized states and extended states coexist and intertwine, thus lacking explicit energy separations. However, as the interchain couplings increase to a certain strength, exact multiple mobility edges emerge. This prediction is clearly verified by concrete numerical calculations of the fractal dimension $FD$ and the scaling index $\beta$. Moreover, we show that the combination of quasiperiodicity and the staggered nonreciprocity can be utilized to design and realize quantum states of various configurations. Our results reveal a brief and general scheme to implement exact multiple mobility edges for synthetic materials engineering.

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• Anderson localization
• Disordered systems
• Non-Hermitian systems
• Exact diagonalization
• Fractal dimension characterization