Scaled Tight-Binding Crystal
- URL: http://arxiv.org/abs/2307.06158v1
- Date: Wed, 12 Jul 2023 13:31:05 GMT
- Title: Scaled Tight-Binding Crystal
- Authors: Peter Schmelcher
- Abstract summary: Local symmetry dynamics has been used to demonstrate the evolution of discrete symmetries in one-dimensional chains.
Here we go one step further and show that the unboundedness of this dynamics can lead to chains that consist of subunits of ever increasing lengths.
Mapping this scaled chain onto a corresponding tight-binding Hamiltonian we investigate its spectral and transmission properties.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The concept of local symmetry dynamics has recently been used to demonstrate
the evolution of discrete symmetries in one-dimensional chains leading to
emergent periodicity. Here we go one step further and show that the
unboundedness of this dynamics can lead to chains that consist of subunits of
ever increasing lengths which results in a scaled chain. Mapping this scaled
chain onto a corresponding tight-binding Hamiltonian we investigate its
spectral and transmission properties. Varying the off-diagonal coupling the
eigenvalue spectrum shows different branches with characteristic transitions
and peaks in the corresponding density of states. The fluctuations of the
energy levels exhibit a hierarchy of minigaps each one accompanied by a
characteristic sequence of energy spacings. We develop a local resonator model
to describe the spectral properties and gain a deeper understanding of it in
the weak to intermediate coupling regime. Eigenstate maps together with the
inverse participation ratio are used to unravel the characteristic
(de-)localization properties of the scaled chain with varying coupling
strength. Finally we probe the energy-dependent transmission profile of the
scaled chain.
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