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A quote from http://en.wikipedia.org/wiki/Symmetry_protected_topological_order : The SPT order (for both frermionic and bosonic systems) has the following defining properties: Distinct SPT states with a given symmetry cannot be smoothly deformed into each other without a phase transition, if the deformation preserves the symmetry. However, they all can ...


1

Yes, this is a known problem in the condensed matter community. There are two different definitions of short range entangled (SRE) states. The key difference is whether the fermion symmetry protected topological (SPT) state belongs to the SRE state. Strictly speaking, the fermion state is not SRE, because fermion statistics is already a phenomenon of long ...


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No, the sign of the gap does not represent particle-hole symmetry. The superconducting gap simply being non-zero automatically encodes the existence of particle-hole symmetry. Variations in the sign of the gap in the Brillouin zone (BZ) determines whether a superconductor is topologically trivial or non-trivial. However, topological or not, a superconductor ...



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