Renormalization Group for the Octagonal Quasi-Periodic Tiling

Clément Sire (1, 2) , J Bellissard (3, 4)

1 PhyStat - Physique Statistique des Systèmes Complexes (LPT)
2 LPT - Laboratoire de Physique Théorique
3 CPT - Centre de Physique Théorique - UMR 7332
4 CPT - Centre de Physique Théorique - UMR 6207

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Matière Condensée [cond-mat]

Clément Sire, J Bellissard. Renormalization Group for the Octagonal Quasi-Periodic Tiling. EPL - Europhysics Letters, 1990, 11 (5), pp.439-443. ⟨10.1209/0295-5075/11/5/009⟩. ⟨hal-02382030⟩