we study the on-site model of a new class of one-dimensional quasiperiodic lattices, for which the substitution rules are B --> BA, and A --> BAB. By means of the renormalization-group approach, a interesting multifractal spectral behavior has been found, which has been confirmed by numerical simulation. A Cantor-like energy spectra is obtained by using the Kohmoto-Kadanaff-Tang (KKT) renormalization-group method. Three kinds of wave-function behavior (extended, localized, and intermediate states) are definitely found.
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