Electronic properties of a one-dimensional hierarchical system

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Abstract
The electronic properties of a one-dimensional hierarchical system are studied using a new type of tight-binding model with a hierarchical array of hopping-matrix elements. By means of a renormalization-group approach the energy spectrum and wave functions are obtained. The spectrum constitutes a Cantor set whose global scaling properties are calculated. A multifractal analysis of the wave functions at the center and at the edge of the spectrum is performed. The relevance of the present work to other models is discussed.