Renormalization Group for the Octagonal Quasi-Periodic Tiling
Résumé
PACS. 71.20-Electronic density of states determinations. PACS. 71.25-Nonlocalized single-particle electronic states. PACS. 71.30-Metal-insulator transitions. Abstract.-We study a renormalization group for a tight-binding Hamiltonian on the standard octagonal tiling. Our method can be generalized to any self-similar quasi-crystal in 2D or even 3D. In the limit of large potentials compared to the hopping parameters, there are numerical evidences that the spectrum is a Cantor set with zero Lebesgue measure.
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