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Yes tensor network algorithms have been developed to describe braiding of anyons, Abelian and non-Abelian. The networks are constructed from tensors that explicitly conserve topological charge and the braiding, fusion, and recoupling data are taken as input to the algorithms. This reference: http://arxiv.org/pdf/1311.0967.pdf describes how to use the Time ...

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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 in one way or another to anyon braiding, to be more precise, the $S$ and $T$ matrices. Here $T$ matrix is a diagonal matrix whose diagonal entries are the ...

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The pentagon and hexagon equations are consistency equations for the fusion and braiding of anyons. They should be satisfied by anyons realized in a gapped, local Hamiltonian. If you do not find solutions, then according to our current understanding of topological phase, yes, such anyons do not exist (in the sense that can not be realized by gapped, local ...

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