Analytical results for Scaling Properties of the Spectrum of the Fibonacci Chain

Details Analytical results for Scaling Properties of the Spectrum of the Fibonacci Chain Analytical results for Scaling Properties of the Spectrum of the Fibonacci Chain

1995-02-16

arxiv.org/abs/cond-mat/9502068v1

Physics

Condensed Matter

12 pages Revtex, 1 figure available upon request

Scientific paper

We solve the approximate renormalisation group found by Qiu Niu and Franco Nori(Phys. Rev. Lett. 57 2057(1986)) for a tight-binding hamiltonian on the Fibonacci chain. This enables us to characterize analytically as completely as possible the spectral properties of this model, such as the spectral measure, the bandwidth distribution, the Lebesgue measure exponent, the Hausdorff dimension, the multifractal scaling, the gaps distribution as well as the long time return probability. Our results, qualitatively and quantitatively complete and unify previous works on similar models.

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