Critical eigenstates and their properties in one- and two-dimensional quasicrystals

Critical eigenstates and their properties in one- and two-dimensional quasicrystals We present exact solutions for some eigenstates of hopping models on one- and two-dimensional quasiperiodic tilings and show that they are “critical” states, by explicitly computing their multifractal spectra. These eigenstates are shown to be generically present in 1D quasiperiodic chains, of which the Fibonacci chain is a special case. We then describe properties of the ground states for a class of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker tilings. Exact and numerical solutions are seen to be in good agreement. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

Critical eigenstates and their properties in one- and two-dimensional quasicrystals

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Critical eigenstates and their properties in one- and two-dimensional quasicrystals

Abstract

We present exact solutions for some eigenstates of hopping models on one- and two-dimensional quasiperiodic tilings and show that they are “critical” states, by explicitly computing their multifractal spectra. These eigenstates are shown to be generically present in 1D quasiperiodic chains, of which the Fibonacci chain is a special case. We then describe properties of the ground states for a class of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker tilings. Exact and numerical solutions are seen to be in good agreement.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1098-0121
eISSN
1550-235X
D.O.I.
10.1103/PhysRevB.96.045138
Publisher site
See Article on Publisher Site

Abstract

We present exact solutions for some eigenstates of hopping models on one- and two-dimensional quasiperiodic tilings and show that they are “critical” states, by explicitly computing their multifractal spectra. These eigenstates are shown to be generically present in 1D quasiperiodic chains, of which the Fibonacci chain is a special case. We then describe properties of the ground states for a class of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker tilings. Exact and numerical solutions are seen to be in good agreement.

Journal

Physical Review BAmerican Physical Society (APS)

Published: Jul 26, 2017

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