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For the first part, although it does not quite make sense to ask "the probability to have a Majorana in position x" (there are no "Majorana" in the system; the system only has electrons), the wavefunc …

Strictly speaking, the statement in your question is not quite accurate: the excitations in the quantum double are classified by irreducible representations of D(G), which is a Hopf algebra. Then one …

It is not true that if $\mathbf{k}\neq -\mathbf{k}$ the matrix element $\langle u_i(\mathbf{k}|T|u_j(\mathbf{k})\rangle$ vanishes. Remember that $u(\mathbf{k})$ are Bloch wavefunctions, which are eige …

The statement cited is misleading. If the system is bosonic, and no symmetry is considered, then indeed all gapped Hermitian Hamiltonians are trivial. With symmetry there can be distinct symmetry-prot …

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 …

Q1: Consider the example of a Haldane phase protected by time-reversal symmetry. There is a spin-1/2 on the edge, and to polarize it (so the system is gapped and the ground state is unique) one must b …

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- …

I'll try to answer the last question, which is of course closely related to the first one (in bold font). The existence of half flux quanta is special to Moore-Read state (the paper cited in the OP c …

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 …

The first question is in a system supporting anyons, what are the universal/topologically invariant physical quantities? Our current theoretical understanding is that all such quantities are related i …

I'll offer an alternative route to engineer a Hamiltonian to realize a general 2+1 TQFT. Again working out details is very challenging and have only been done for some special cases. The idea is to us …

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 …