Quantum Diffusion in Separable d-Dimensional Quasiperiodic Tilings

TL;DR

This paper investigates electronic transport in separable quasiperiodic tilings across one to three dimensions, analyzing wave packet dynamics and scaling behavior to understand quantum diffusion in these complex structures.

Contribution

It introduces a detailed analysis of quantum diffusion in higher-dimensional separable quasiperiodic tilings using scaling and renormalization techniques.

Findings

Wave packet mean square displacement exhibits specific scaling laws.

Return probability decays following characteristic power laws.

Lower bounds for wave packet width scaling are established.

Abstract

We study the electronic transport in quasiperiodic separable tight-binding models in one, two, and three dimensions. First, we investigate a one-dimensional quasiperiodic chain, in which the atoms are coupled by weak and strong bonds aligned according to the Fibonacci chain. The associated d-dimensional quasiperiodic tilings are constructed from the product of d such chains, which yields either the square/cubic Fibonacci tiling or the labyrinth tiling. We study the scaling behavior of the mean square displacement and the return probability of wave packets with respect to time. We also discuss results of renormalization group approaches and lower bounds for the scaling exponent of the width of the wave packet.