期刊
PHYSICAL REVIEW A
卷 93, 期 3, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.93.030102
关键词
-
资金
- NSF [DMS-119725, DMS-1410144, DMS-1108736, DMS-1411212]
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 > 1 that the resulting representations of all n-strand braid groups B, are overall phases, even though the ground -state manifolds for n such anyons in the plane are in general Hilbert spaces of dimensions > 1. We observe that degeneracy is all that is needed: For an anyon with quantum dimension > 1 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 > 1. Since non-Abelian statistics presumes degeneracy, degeneracy is more fundamental than non-Abelian statistics.
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