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Mathematicians like to write tensor product, since in many cases (or maybe in all cases) anyon types (simple objects) are indeed irreducible representations of some algebraic object (e.g. Hopf algebra, quantum groups), and irreducible representations of finite groups provide a large family of examples for fusion categories, where $\otimes$ and $\oplus$ ...


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In these modern DMRG algorithms for topological phases, braiding statistics is rarely computed directly. The reason is that it is not clear how to trap a particular anyon in the bulk, and to get braiding statistics requires a careful calculation of adiabatic non-Abelian Berry phase which is often very computationally demanding. Instead, one calculates ...



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