  Quasiholes in certain fractional quantum Hall states are promising candidates
for the experimental realization of non-Abelian anyons. They are assumed to be
localized excitations, and to display non-Abelian statistics when sufficiently
separated, but these properties have not been explicitly demonstrated except
for the Moore-Read state. In this work, we apply the newly developed matrix
product state technique to examine these exotic excitations. For the Moore-Read
and the $\mathbb{Z}_3$ Read-Rezayi states, we estimate the quasihole radii, and
determine the correlation lengths associated with the exponential convergence
of the braiding statistics. We provide the first microscopic verification for
the Fibonacci nature of the $\mathbb{Z}_3$ Read-Rezayi quasiholes. We also
present evidence for the failure of plasma screening in the non-unitary
Gaffnian wave function.
