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Topological Quantum Field Theory (TQFT) is the low energy effective theory for the topological ordered states in real world, such as FQH states. In fact, the name "topological order" was motived from the term "Topological Quantum Field Theory". [See Topological Orders in Rigid States, Xiao-Gang Wen, Int. J. Mod. Phys. B4, 239 (1990) ...


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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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There is a nice pedagogical review of the quantum Hall effect that can be found here. They explain (sketchily) how to derive an effective action describing the bulk of a quantum Hall fluid, which is a topological quantum field theory: Chern-Simons (CS) theory. The main physics which can be gleaned from this is that any defects in the bulk of the fluid could ...



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