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I asked my advisor this exact same question a couple years ago. He said that there's no sense of anyonic statistics in momentum space (or in any basis other than real space). The reason for this is that anyons typically emerge from a microscopic Hamiltonian that is spatially local, and so strictly speaking, anyons are only well-defined when they stay far ...


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The definition of a spin liquid as a spin system "with no spontaneously broken symmetries" is out of date and no longer used, partially for the reason you describe. If you perturb as spin-liquid Hamiltonian by adding small terms that break all the symmetries, then the ground state will still be a spin liquid even though there are no longer any symmetries ...



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