Electrons on one-dimensional quasi-periodic lattices

Abstract

We study electronic states on one-dimensional quasi-periodic lattices numerically by using the tight binding Fibonacci model generated by the Fibonacci substitution rule. It is found that the electronic states are critical, that is, intermediate between the localized and extended states. This critical state is characterized by the branching rule of the energy spectra and the inverse power law behavior of the level spacings. The Harper model with an incommensurate cosine potential, and quasi-periodic lattice models generated by other substitution rules are examined. Phonon problem in the quasi-periodic lattice is also discussed.