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Let us consider the S matrix of Ising anyons as an example: $S_{\sigma\sigma}=0$. To be more precise, suppose we have four $\sigma$'s, labeled as $1,2,3,4$. We assume $1$ and $2$ are in a definite fu …

The non-interacting classification was obtained in the seminal "periodic table" papers by Kitaev and Ryu/Snyder/Furusaki/Ludwig. The interacting classification of 2D fermionic SPT phases with time-rev …

The relevant part of the sum as $\sum_{k^*,s_1,s_2}\delta_{k^*,s_1s_2}d_{s_1}d_{s_2}B^k_P$ Let me assume that the fusion category has no multiplicities, so $N_{ab}^c=0,1$, which I think Levin and We …

For 2D chiral p-wave, it has been shown that the Berry phase contribution vanishes and therefore the exchange statistics is entirely given by the monodromy. This was done in http://arxiv.org/abs/cond- …

The splitting is not just $F$ symbols. There are also non-universal tunneling amplitudes $\Gamma_e$, which will compensate for the gauge transformations of $F$. In the end of the day, what we may lear …

https://arxiv.org/abs/1205.5792 The first example in the paper is $C=3$ on a triangular lattice with two orbitals per site. It is essentially three-layers of Haldane's honeycomb lattice model, but sta …

When the Chern numbers of the two bands go from $(1,-1)$ to $(-1,1)$, the Chern number of the occupied band changes sign. Even though the number of chiral edge modes is the same, they have opposite ch …

1 has been partially solved in the following sense: Iridates amazingly have Kitaev interaction (among other interactions). 2 a lot has been known about this kind of phenomena, now part of the story of …

To have time-reversal symmetry, there needs to be a unitary operator $U$ such that $ U\sigma^x U^{-1}=-\sigma^x, U\sigma^y U^{-1}= \sigma^y, U\sigma^z U^{-1}=\sigma^z$. These follow from $T=UK$, and I …

The definition in terms of LU transformations is more fundamental. In the general case, we believe that topological orders are described by modular tensor categories (MTC), and the equivalence of topo …

I'm just going to put a slightly more general remark, essentially the same as the answer by Norbert. The condensation of Lagrangian subalgebra (it is not just a set, really an algebra satisfying sever …

It seems that you thought $\Phi_0$ is a trivial SPT while $\Phi$ is nontrivial. This does not make sense without defining the symmetry transformation. The fact that $\Phi=U\Phi_0$ means both are produ …

One first needs to define what it means for a state to be topological when the system is gapless. This is not an easy question! I don't think there is a unified answer at the moment. I'll give some …

This paper https://arxiv.org/abs/1904.05491 proves that there can not be any net energy current in equilibrium state on a lattice system, which implies that left-moving and right-moving modes must bal …

Well it depends on what you mean by "exactly solvable". Many people would consider any quadratic Hamiltonian(i.e. non-interacting) exactly solvable, so the BCS Hamiltonian of a p+ip superconductor alr …