تقرير
Multifractal Properties of Tribonacci Chains
| العنوان: | Multifractal Properties of Tribonacci Chains |
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| المؤلفون: | Krebbekx, Julius, Moustaj, Anouar, Dajani, Karma, Smith, Cristiane Morais |
| المصدر: | Phys. Rev. B 108, 104204 (2023) |
| سنة النشر: | 2023 |
| المجموعة: | Condensed Matter |
| مصطلحات موضوعية: | Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics |
| الوصف: | We introduce two 1D tight-binding models based on the Tribonacci substitution, the hopping and on-site Tribonacci chains, which generalize the Fibonacci chain. For both hopping and on-site models, a perturbative real-space renormalization procedure is developed. We show that the two models are equivalent at the fixed point of the renormalization group flow, and that the renormalization procedure naturally gives the Local Resonator Modes. Additionally, the Rauzy fractal, inherent to the Tribonacci substitution, is shown to serve as the analog of conumbering for the Tribonacci chain. The renormalization procedure is used to repeatedly subdivide the Rauzy fractal into copies of itself, which can be used to describe the eigenstates in terms of Local Resonator Modes. Finally, the multifractal dimensions of the energy spectrum and eigenstates of the hopping Tribonacci chain are computed, from which it can be concluded that the Tribonacci chains are critical. Comment: 23 pages, 15 figures, article, comments are welcome |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevB.108.104204 |
| URL الوصول: | http://arxiv.org/abs/2304.11144 |
| رقم الأكسشن: | edsarx.2304.11144 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevB.108.104204 |
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