Pubs.GISS: Abstract of Holzer 1991

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Holzer 1991

Holzer, M., 1991: Multifractal wave functions on a class of one-dimensional quasicrystals: Exact f(α) curves and the limit of dilute quasiperiodic impurities. Phys. Rev. B, 44, 2085-2091, doi:10.1103/PhysRevB.44.2085.

We calculate the exact multifractal scaling spectrum f(α) for the center-band wave function of an off-diagonal tight-binding Hamiltonian defined on the "precious-mean" (PM) lattices, i.e., the class of one-dimensional quasiperiodic lattices generated recursively by (A,B) → (AⁿB,A). We find that, in the limit of dilute quasiperiodic "impurities," n → ∞, the center-band wave function approaches a Bloch state for n even, whereas for n odd a limiting "critical" state is approached. This difference between even and odd n is explained in terms of the convergence properties of the spectrum of the same Hamiltonian defined on periodic extensions of finite-iteration approximants to the PM lattices. For both even and odd n, corrections to the n=∞ limit go to zero like 1/ln(n). The scaling properties of generic eigenstates are discussed.