Comment on "Topological equivalence of crystal and quasicrystal band structures"
arXiv:1308.2378
Abstract
Madsen et al. [arXiv:1307.2577] claim that one-dimensional insulating crystals and one-dimensional insulating quasicrystals are topologically equivalent and, thus, trivial. In this comment, we clarify that in topological classification of one-dimensional systems, quasiperiodicity plays a role similar to that of a symmetry. Hence, periodic systems are out of the quasiperiodic topological space, and the equivalence between quasicrystals and crystals becomes immaterial.
arXiv comment3 pages