Analytical results for Scaling Properties of the Spectrum of the Fibonacci Chain
arXiv:cond-mat/9502068 · doi:10.1103/PhysRevLett.74.5248
Abstract
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.
12 pages Revtex, 1 figure available upon request
Cited by in corpus (24)
- Fermi Surface reconstruction in the CDW state of CeTe3 observed by photoemission
- Physical nature of critical wave functions in Fibonacci systems
- Anomalous transport: a mathematical framework
- Critical eigenstates and their properties in one and two dimensional quasicrystals
- Fractal dimensions of the wavefunctions and local spectral measures on the Fibonacci chain
- The Proximity Effect in a Superconductor-Quasicrystal Hybrid Ring
- Local symmetry theory of resonator structures for the real-space control of edge states in binary aperiodic chains
- Hofstadter Rules and Generalized Dimensions of the Spectrum of Harper's Equation
- Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings
- Nonmonotonic crossover and scaling behaviors in a disordered 1D quasicrystal
- Universal Route for the Emergence of Exceptional Points in PT-Symmetric Metamaterials with Unfolding Spectral Symmetries
- Topological quantum optical states in quasiperiodic cold atomic chains
- Analytical Results for Multifractal Properties of Spectra of Quasiperiodic Hamiltonians near the Periodic Chain
- Effects of Disorder in the Fibonacci Quasicrystal
- Gap structure of 1D cut and project Hamiltonians
- Critical Level Statistics of the Fibonacci Model
- Self-similarity under inflation and level statistics: a study in two dimensions
- The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
- Quantum chaos in small quantum networks
- Superconducting properties of Fibonacci chains with enhanced superconducting pairing at the boundaries
- Missing link between the 2D Quantum Hall problem and 1D quasicrystals
- Persistent current and Drude weight in one-dimensional rings with substitution potentials
- Chaos-based Potentials in the One-dimensional Tight-binding Model Probed by the Inverse Participation Ratio
- Superconducting order parameter in aperiodic binary systems