Abstract
Energy spectral properties in one-dimensional quasi-crystalline and incommensurate systems are studied numerically. It is known that the critical state, which is intermediate between the localized and the extended ones, occurs in these models. We find that those critical states are well characterized in common by the branching rule of the spectra and the inverse-power-law behavior of the level spacings. Special emphasis is put on the relation of the branching rule to the quasi-periodicity of the underlying lattice and the sensitivity of the level-spacing distribution to the electronic state, namely whether it is localized, critical or extended.
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