Effects of Disorder in the Fibonacci Quasicrystal

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, to some extent, the addition of multiple, weak impurities can be treated by superposing the individual contributions together and ignoring nonlinear effects. This means that 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 different localisation behaviours of the wavefunctions. This is manifested through a symmetry in the wavefunction amplitude map, expressed in terms of conumbers, and through the inverse participation ratio. For the latter, we find that its average of states can also be grouped in terms of the renormalization path of the site at which the impurity has been placed.