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تسجيل مستخدم جديدHidden dualities in 1D quasiperiodic lattice models
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We find that quasiperiodicity-induced localization-delocalization transitions in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-Andre model. For a given energy window, such duality is locally defined near the transition and can be explicitly determined by considering commensurate approximants. This relies on the construction of an auxiliary 2D Fermi surface of the commensurate approximants as a function of the phase-twisting boundary condition and of the phase-shifting real-space structure. Considering widely different families of quasiperiodic 1D models, we show that, around the critical point of the limiting quasiperiodic system, the auxiliary Fermi surface of a high-enough-order approximant converges to a universal form. This allows us to devise a highly-accurate method to compute mobility edges and duality transformations for generic 1D quasiperiodic systems through their commensurate approximants. To illustrate the power of this approach, we consider several previously studied systems, including generalized Aubry-Andre models and coupled Moire chains. Our findings bring a new perspective to examine quasiperiodicity-induced localization-delocalization transitions in 1D, provide a working criterion for the appearance of mobility edges, and an explicit way to understand the properties of eigenstates close and at the transition.
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