227 research outputs found
Degeneracy Implies Non-abelian Statistics
A non-abelian anyon can only occur in the presence of ground state degeneracy
in the plane. It is conceivable that for some strange anyon with quantum
dimension that the resulting representations of all -strand braid
groups are overall phases, even though the ground state manifolds for
such anyons in the plane are in general Hilbert spaces of dimensions . We
observe that degeneracy is all that is needed: for an anyon with quantum
dimension the non-abelian statistics cannot all be overall phases on the
degeneracy ground state manifold. Therefore, degeneracy implies non-abelian
statistics, which justifies defining a non-abelian anyon as one with quantum
dimension . Since non-abelian statistics presumes degeneracy, degeneracy is
more fundamental than non-abelian statistics.Comment: State the main result as a theorem and add several clarification
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