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

TL;DR

This paper investigates quantum diffusion in quasiperiodic labyrinth tilings across multiple dimensions, revealing anomalous diffusion behaviors governed by the underlying quasiperiodic structure, using an extended renormalization group approach.

Contribution

It extends a renormalization group method to analyze wave-packet dynamics in higher-dimensional quasiperiodic systems, including silver-mean and labyrinth tilings, demonstrating the influence of quasiperiodicity.

Findings

Anomalous diffusion observed in quasiperiodic systems.

Wave-packet dynamics governed by quasiperiodic structure in strong modulation regime.

Extension of RG approach to higher-dimensional and different quasiperiodic sequences.

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.