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The "topological" in "topological order" and the "topological" in "topological insulator" have different meanings. The 'topological' in topological order means 'robust against ANY local perturbations'. The "topological" in "topological insulator" means 'robust against some local perturbations that respect certain symmetry'. In fact the properties of ...


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It belongs to the symmetry class of no symmetry. i.e. the only symmetry is the fermion-number-parity conservation $Z_2^f$, which is always the symmetry of fermionic systems. See my paper http://arxiv.org/abs/1111.6341 for a discussion on the full-symmetry group $G_f$ for fermion systems.


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The brief answer is yes, they do have topological degeneracy. My understanding is that if you only focus on the surface topological order with some symmetry given by the bulk symmetry protected topological (SPT) state, there is nothing wrong with that symmetry enriched topological order (SET) states. That means they also have all the properties as the usual ...



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