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field theory and unitary modular tensor category theory [or unitary braided fusion category], the latter of which describes the rules governing the fusion and braiding process of topological excitations (anyons …

particles, if we braid $z_i$ CCW around $z_j$, we have $\Psi\to e^{i\pi p/q}\Psi$ while for a CW braid, we have $\Psi\to e^{-i\pi p/q}\Psi$, so this represent a wavefunction of $N$ identical abelian anyons …

generality of this phenomenon: Given a 2D quantum double phase described by a Drinfeld center $Z(\mathcal{C})$ (where $\mathcal{C}$ is a unitary fusion category), which type of topological excitations (anyons …

I'm familiar with how fusion categories describe the fusion of point-like excitations, and how braided fusion categories describe the fusion of anyons in 2+1D topological order. …

An important open mathematical problem in the theoretical foundation of topological order is to prove that the universal properties (braiding and fusion) of point-like excitations in any gapped phase …

It is a well-established fact that topological excitations (anyons) in 2D topologically-ordered systems are described by unitary modular tensor categories, see, e.g., Appendix E in Kitaev (2006). …