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Localization properties of particles in one-dimensional incommensuratelattices without interaction are investigated with models beyond thetight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2model with finite next-nearest-neighbor hopping t_2, we find the localizationproperties qualitatively different from those of the AA model, signaled by theappearance of mobility edges. We then further go beyond the tight-bindingassumption and directly study the system based on the more fundamentalsingle-particle Schr\"odinger equation. With this approach, we also observe thepresence of mobility edges and localization properties dependent onincommensuration.

Localization in one-dimensional incommensurate lattices beyond the Aubry-Andr\'e model