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arXiv · 1204.4017

Renormalization Group Approach for the Wave Packet Dynamics in Golden-Mean and Silver-Mean Labyrinth Tilings

Stefanie Thiem·Michael Schreiber
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Abstract

We study the quantum diffusion in quasiperiodic tight-binding models in one, two, and three dimensions. First, we investigate a class of one-dimensional quasiperiodic chains, in which the atoms are coupled by weak and strong bonds aligned according to the metallic-mean sequences. The associated generalized labyrinth tilings in d dimensions are then constructed from the direct product of d such chains, which allows us to consider rather large systems numerically. The electronic transport is studied by computing the scaling behavior of the mean-square displacement of the wave packets with respect to the time. The results reveal the occurrence of anomalous diffusion in these systems. By extending a renormalization group approach, originally proposed for the golden-mean chain, we show also for the silver-mean chain as well as for the higher-dimensional labyrinth tilings that in the regime of strong quasiperiodic modulation the wave-packet dynamics are governed by the underlying quasiperiodic structure.

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Stefanie Thiem, Michael Schreiber. 2012-04-18. Renormalization Group Approach for the Wave Packet Dynamics in Golden-Mean and Silver-Mean Labyrinth Tilings. https://doi.org/10.1103/physrevb.85.224205

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