The determination of the mobility edge (ME)—the critical energy threshold separating extended and localized quantum states—remains a central challenge in the study of Anderson transitions, particularly within complex non-Hermitian systems where conventional Hermitian techniques often fail. While the standard Aubry–André–Harper model provides a paradigmatic example of localization in one-dimensional quasiperiodic systems, the precise analytical determination of MEs in models breaking standard self-duality has proven elusive. This comprehensive report presents a rigorous and exhaustive theoretical framework for a class of non-Hermitian quasiperiodic network models that incorporate both periodic and quasiperiodic sublattices, nonreciprocal hopping, and complex quasiperiodic potentials. By systematically integrating out periodic degrees of freedom, we unveil a “hidden” self-duality in the effective Hamiltonian, a symmetry absent in the original description. We derive exact, energy-dependent MEs defined by the effective potential $g\left(E\right)V$ and eigenenergy $f\left(E\right)$. We demonstrate that states satisfying $g\left(E\right)=0$ are intrinsically extended, allowing for the precise analytical prediction of ME trajectories. Furthermore, we generalize this duality-based approach to systems exhibiting nonuniform (Su–Schrieffer–Heeger type) and long-range (exponentially decaying) hopping. This work not only provides exact analytical solutions for a broad class of previously intractable models but also offers a unifying perspective on the interplay between non-Hermiticity, topology, and quasiperiodic disorder, with significant implications for experimental realizations in photonic and acoustic metamaterials.

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• Anderson localization
• Non-Hermitian systems
• Quasicrystals
• Tight-binding model