Spectral structure for a class of one-dimensional three-tile quasilattices

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Abstract
Using a decomposition-decimation method based on the renormalization-group technique, we have studied the spectral structure of a class of one-dimensional three-tile quasiperiodic lattice models, for which the (concurrent) substitution rules are S→M, M→L, and L→LS, where S, M, and L represent, respectively, the short, medium, and long tiles. Branching rules for the electronic energy spectrum have been analytically obtained and confirmed by numerical simulations. It is found that three kinds of branching patterns alternately appear in the spectrum, which displays a kind of self-similarity very different from the trifurcating self-similarity of one-dimensional Fibonacci quasilattices.