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In topologically ordered quantum states of matter in 2+1D (space-time dimensions), the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property which is directly related to global transformations of the ground-state wavefunctions on a torus (the modular transformations).
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2014
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Xie Chen, Yuan-Ming Lu, and Ashvin Vishwanath, “Symmetry protected topological phases from decorated domain walls,” Nature Communications, 5
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