Journal
PHYSICAL REVIEW B
Volume 96, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.96.045138
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We present exact solutions for some eigenstates of hopping models on one-and two-dimensional quasiperiodic tilings and showthat they are critical states, by explicitly computing their multifractal spectra. These eigenstates are shown to be generically present in 1D quasiperiodic chains, of which the Fibonacci chain is a special case. We then describe properties of the ground states for a class of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker tilings. Exact and numerical solutions are seen to be in good agreement.
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