Effects of Disorder in the Fibonacci Quasicrystal

Abstract

We study the properties of the one-dimensional Fibonacci chain, subjected to the placement of on-site impurities. The resulting disruption of quasiperiodicity can be classified in terms of the renormalization path of the site at which the impurity is placed, which greatly reduces the possible amount of disordered behavior that impurities can induce. Moreover, it is found that the addition of multiple weak impurities can be treated by superposing the individual contributions together. In that case, a transition regime between quasiperiodic order and disorder exists, in which some parts of the system still exhibit quasiperiodicity, while other parts start to be characterized by the localisation of the wavefunctions. This behavior is manifested through a symmetry in the wavefunction amplitude map, expressed in terms of conumbers.