Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling

Details Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling

1998-05-25

arxiv.org/abs/cond-mat/9805321v1

Phys. Rev. B 58 (1998) 13482-13490

Physics

Condensed Matter

24 pages, REVTeX, 13 PostScript figures included

Scientific paper

10.1103/PhysRevB.58.13482

We investigate exact eigenstates of tight-binding models on the planar rhombic Penrose tiling. We consider a vertex model with hopping along the edges and the diagonals of the rhombi. For the wave functions, we employ an ansatz, first introduced by Sutherland, which is based on the arrow decoration that encodes the matching rules of the tiling. Exact eigenstates are constructed for particular values of the hopping parameters and the eigenenergy. By a generalized ansatz that exploits the inflation symmetry of the tiling, we show that the corresponding eigenenergies are infinitely degenerate. Generalizations and applications to other systems are outlined.

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