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Within the framework of the Aubry-Andre model, one kind of self-dual quasiperiodic lattice, it is known that a sharp transition occurs from \emph{all} eigenstates being extended to \emph{all} being localized.
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It should be mentioned that several QP models with energy-dependent mobility edges have been found [ 18 , 20 , 25 ] . In these QP systems, the mobility edges come to appear because the self duality is broken via some other effects, e.g
Cited in the paper.
In this work, we focus on the property of lattices with the modulation strength around λ = 2.0 \lambda=2.0 . Actually, there is a pure insulator phase when λ \lambda is large enough, which is related to the pure metal phase at small modulation. The reason lies in the fact that the system is self-dual and λ = 2.0 \lambda=2.0 is the dual point, therefore the localization property at λ \lambda corresponds inversely to that of 4 / λ 4/\lambda through the Fourier transformation. See Supplemental Material for detailed descriptions about the global phase diagram and the illustration of self-duality of our model
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Mobility edges in 1D disordered systems have been realized only in the case with statistical correlations, e.g
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