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One-dimensional quasiperiodic systems, such as the Harper model and theFibonacci quasicrystal, have long been the focus of extensive theoretical andexperimental research. Recently, the Harper model was found to be topologicallynontrivial. Here, we derive a general model that embodies a continuousdeformation between these seemingly unrelated models. We show that thisdeformation does not close any bulk gaps, and thus prove that these models arein fact topologically equivalent. Remarkably, they are equivalent regardless ofwhether the quasiperiodicity appears as an on-site or hopping modulation. Thisproves that these different models share the same boundary phenomena andexplains past measurements. We generalize this equivalence to anyFibonacci-like quasicrystal, i.e., a cut and project in any irrational angle.

Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model