Abstract:
In this paper we investigated the electronic energy spectrum of the one-dimensional quasi-periodic Periodic-Doubling lattice under the tight-binding approximation by means of a renormalization-group procedure. We calculated the high-degenerated energy levels and the integrated density if state (DOS). We also undertook numerical calculations based on Dean's negative eigenvalue theory, which shows that the integrated DOS of the Period-Doubling lattice changes abruptly at certain energy levels, while in the periodic case it changes smoothly with energy. The analytical and the numerical results were compared. It was found that the two kinds of results agree very well.