Do quasicrystals exhibit topological order?

Physics Asked on December 19, 2020

According to the book Quantum Information meets Quantum Matter, ordered phases can either be described by a Landau free energy: symmetry-breaking ordered phases; or there are different ways in which local Hamiltonians can give rise to global patterns: topological order.

Quasicrystals don’t seem to be symmetry-breaking, at least not the translational symmetry.

On the other hand, they seem to be somewhat analogous to Spin Liquids, which are an example of a topological order; On the other hand, I find it hard to assign a ‘topological invariant’ to them.

So what kind of order do quasicrystals exhibit?

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