Critical eigenstates and their properties in one and two dimensional quasicrystals
Disordered Systems and Neural Networks
2017-08-02 v1 Mesoscale and Nanoscale Physics
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.
Keywords
Cite
@article{arxiv.1706.06796,
title = {Critical eigenstates and their properties in one and two dimensional quasicrystals},
author = {Nicolas Macé and Anuradha Jagannathan and Pavel Kalugin and Rémy Mosseri and Frédéric Piéchon},
journal= {arXiv preprint arXiv:1706.06796},
year = {2017}
}