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## New answers tagged topological-order

3

How to obtain this braiding matrix from Non-Abelian Chern-Simon theory? To obtain braiding matrix $U^{ab}$ for particle $a$ and $b$, we first need to know the dimension of the matrix. However, the dimension of the matrix for Non-Abelian Chern-Simon theory is NOT determined by $a$ and $b$ alone. Say if we put four particles $a,b,c,d$ on a sphere, the ...

2

The (unitary) "phase" factor for non-Abelian anyons satisfies the (non-Abelian) Knizhnik-Zamolodchikov equation: $$\big (\frac{\partial}{\partial z_{\alpha}} + \frac{1}{2\pi k} \sum_{\beta \neq \alpha} \frac{Q^a_{\alpha}Q^a_{\beta}}{z_{\alpha} - z_{\beta}}\big )U(z_1, ....,z_N) = 0$$ Where $z_{\alpha}$ is the complex plane coordinate of the particle ...

1

The short answer is, yes, the chiral edge state is determined by bulk topological property. It is known as bulk-edge correspondence. The paper you should read is: Protected edge modes without symmetry - 1301.7355. Generically, to determine whether the edge states are robust is by determining whether the edge states are protected'' by any of the three ...

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