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A very late answer, but for symmetry-protected topological (SPT) phases, I believe it is true (certainly, no counterexamples are known) that the boundary is "non-trivial" if and only if the bulk is a non-trivial SPT phase. Here "non-trivial" boundary has a very specific meaning. A boundary is "non-trivial" if there is NO symmetry-respecting terms that we can ...


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The model of Levin and Gu is built out of products of the spin-1/2 operators $S_i^x$, $S_i^y$ and $S_i^z$ at each site $i$. These operators commute with each other at different sites ($[S_i^\alpha, S_j^\beta] = 0$ for $i \neq j$), which is the reason why we say this model is bosonic, and the SPT phases in this model are bosonic SPT's. By constrast, a ...


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I don't think the provided comment gives the right answer. Topological insulators is the bigger group and Chern insulator are a subgroup of that. This means that every Chern insulator is a topological insulator, but not every topological insulator is a Chern insulator. Can maybe someone confirm that this is indeed true? In general a topological insulator is ...


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I think the first helpful fact to clarify is that there are two different kinds of topological phases: there are so-called Symmetry Protected Topological (SPT) Phases (displaying 'symmetry protected topological order') and there are (intrinsic) Topological Phases (displaying '(intrinsic) topological order'). As some quick examples: topological insulators and ...



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