Quasicrystals have recently been found to be topologically nontrivial in one-dimension. In particular, the Harper (or Aubry-Andre) model was found to be associated with Chern numbers and topological boundary states. We will show that the Fibonacci quasicrystal, as well as any Fibonacci-like quasicrystal, is topologically equivalent to the Harper model, since they can be extended to equivalent quantum Hall systems [1]. This equivalence is verified experimentally through the absence of a phase transition when deforming between them [2].

[1] Phys. Rev. Lett. 109, 116404 (2012)

[2] arXiv:1211.4476