J. Phys. I France
Volume 4, Numéro 10, October 1994
Page(s) 1513 - 1525
DOI: 10.1051/jp1:1994204
J. Phys. I France 4 (1994) 1513-1525

Electronic properties of the octagonal tiling : a new renormalization-group calculation

J. X. Zhong1, 2 and R. Mosseri1

1  Groupe de Physique des solides, Université Paris 7 et 6. Tour 23, 2 place Jussieu, 75251 Paris Cedex 05, France
2  Laboratory of Modern Physics, Xiangtan University, 411105 Hunan, P. R. China

(Received 21 April 1994, received in final form in 22 June 1994, accepted 30 June 1994)

We present a new renormalization-group calculation of the octagonal tiling excitation spectrum. Two new self-similar octagonal tilings are introduced, a triangle-kite and a triangle-dart tiling, which are entangled with the standard rhombus-square tiling. The decimation procedure involved in the renormalization group calculation transforms each tiling onto a different one and goes back to the (rescaled) original tiling after three steps. The local and average density of states are calculated. In the case of a Laplacian-like tight-binding Hamiltonian, on the standard rhombussquare octagonal tiling, our results compare reasonably well to numerically derived spectra and improve some previous renormalization group calculations. In the pure hopping case, the renormalization is shown to be inaccurate by comparing to numerical density of states obtained by a continued fraction method.

© Les Editions de Physique 1994

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