1204.3517 (Yaacov E. Kraus et al.)

Topological Equivalence Between The Fibonacci Quasicrystal and The
Harper Model    [PDF]

Yaacov E. Kraus, Oded Zilberberg

One-dimensional quasi-periodic systems, such as the Harper model and the Fibonacci quasicrystal, have long been the focus of extensive theoretical and experimental research. Recently, the Harper model was found to be topologically non-trivial. Here, we derive a general model that embodies a continuous deformation between these seemingly unrelated models. We show that this deformation does not close any bulk gaps, and thus prove that these models are in fact topologically equivalent. Remarkably, they are equivalent regardless of whether the quasi-periodicity appears as a diagonal or off-diagonal modulation. This proves that these different models share the same boundary phenomena and explains past measurements. We generalize this equivalence to additional Fibonacci-like quasi-periodic patterns.

View original: http://arxiv.org/abs/1204.3517