Eur. Phys. J. B 83, 415-421 (2011)
https://doi.org/10.1140/epjb/e2011-20323-7

Regular Article

Generalized inverse participation numbers in metallic-mean quasiperiodic systems

Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany

^a e-mail: stefanie.thiem@physik.tu-chemnitz.de

Received: 27 April 2011
Received in final form: 5 September 2011
Published online: 10 October 2011

Abstract

From the quantum mechanical point of view, the electronic characteristics of quasicrystals are determined by the nature of their eigenstates. A practicable way to obtain information about the properties of these wave functions is studying the scaling behavior of the generalized inverse participation numbers Z_q ~ N ^{− D_q(q − 1)} with the system size N. In particular, we investigate d-dimensional quasiperiodic models based on different metallic-mean quasiperiodic sequences. We obtain the eigenstates of the one-dimensional metallic-mean chains by numerical calculations for a tight-binding model. Higher dimensional solutions of the associated generalized labyrinth tiling are then constructed by a product approach from the one-dimensional solutions. Numerical results suggest that the relation holds for these models. Using the product structure of the labyrinth tiling we prove that this relation is always satisfied for the silver-mean model and that the scaling exponents approach this relation for large system sizes also for the other metallic-mean systems.