Renormalization Group Approach for the Wave Packet Dynamics in Golden-Mean and Silver-Mean Labyrinth Tilings
arXiv:1204.4017 · doi:10.1103/PhysRevB.85.224205
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.
15 pages, 20 figures
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Cited by in corpus (10)
- Non-equilibrium quantum relaxation across a localization-delocalization transition
- Nonequilibrium quench dynamics in quantum quasicrystals
- Local symmetry dynamics in one-dimensional aperiodic lattices
- Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings
- Nonmonotonic crossover and scaling behaviors in a disordered 1D quasicrystal
- Topological charge pumping in quasiperiodic systems characterized by Bott index
- Quantum and Spectral Properties of the Labyrinth Model
- Properties of the Ammann-Beenker tiling and its square approximants
- The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
- Absolutely continuous energy bands and extended electronic states in an aperiodic comb-shaped nanostructure