Spectral Properties of Two Coupled Fibonacci Chains
- URL: http://arxiv.org/abs/2208.05178v2
- Date: Mon, 26 Jun 2023 14:03:19 GMT
- Title: Spectral Properties of Two Coupled Fibonacci Chains
- Authors: Anouar Moustaj, Malte R\"ontgen, Christian V. Morfonios, Peter
Schmelcher and Cristiane Morais Smith
- Abstract summary: We study the eigenvalues and eigenstates of two identical Fibonacci chains coupled to each other in different ways.
The proposed setup allows for an experimental realization, e.g., with evanescently coupled waveguides, electric circuits, or by patterning an anti-lattice with adatoms on a metallic substrate.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Fibonacci chain, i.e., a tight-binding model where couplings and/or
on-site potentials can take only two different values distributed according to
the Fibonacci word, is a classical example of a one-dimensional quasicrystal.
With its many intriguing properties, such as a fractal eigenvalue spectrum, the
Fibonacci chain offers a rich platform to investigate many of the effects that
occur in three-dimensional quasicrystals. In this work, we study the
eigenvalues and eigenstates of two identical Fibonacci chains coupled to each
other in different ways. We find that this setup allows for a rich variety of
effects. Depending on the coupling scheme used, the resulting system (i)
possesses an eigenvalue spectrum featuring a richer hierarchical structure
compared to the spectrum of a single Fibonacci chain, (ii) shows a coexistence
of Bloch and critical eigenstates, or (iii) possesses a large number of
degenerate eigenstates, each of which is perfectly localized on only four sites
of the system. If additionally, the system is infinitely extended, the
macroscopic number of perfectly localized eigenstates induces a perfectly flat
quasi band. Especially the second case is interesting from an application
perspective, since eigenstates that are of Bloch or of critical character
feature largely different transport properties. At the same time, the proposed
setup allows for an experimental realization, e.g., with evanescently coupled
waveguides, electric circuits, or by patterning an anti-lattice with adatoms on
a metallic substrate.
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