Degeneracy Implies Non-abelian Statistics Institutional Repository Document uri icon


  • 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 $B_n$ 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.

author list (cited authors)

  • Rowell, E. C., & Wang, Z.

complete list of authors

  • Rowell, Eric C||Wang, Zhenghan

publication date

  • August 2015