New answers tagged

1

TQFTs by definition satisfy cutting and gluing axioms. Roughly speaking, you should be able to obtain the partition function of the TQFT on a general (closed) manifold by cutting the manifold into small, elementary pieces which we understand, and then the partition function can be calculated from assembling the pieces together. This holds very generally in ...


2

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 ...


0

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 ...


2

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 ...


2

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 ...



Top 50 recent answers are included