  Non-Abelian (NA) fractional topological states with quasi-particles obeying
NA braiding statistics have attracted intensive attentions for both its
fundamental nature and the prospect for topological quantum computation. To
date, there are many models proposed to realize the NA fractional topological
states, such as the well-known Moore-Read quantum Hall states and the
Non-Abelian fractional Chern insulators (NA-FCIs). Here, we investigate the
NA-FCI in disk geometry with three-body hard-core bosons loaded into a
topological flat band. This stable $\nu = 1$ bosonic NA-FCI is characterized by
the edge excitations and the ground-state angular momentum. Based on the
generalized Pauli principle and the Jack polynomials, we successfully construct
a trial wave function for the NA-FCI. Moreover, a $\nu = 1/2$ Abelian FCI state
emerges with the increase of the on-site interaction and it can be identified
with the help of the trial wave function as well. Our findings not only lead to
an optimal wave function for the NA-FCI, but also directly provide an effective
approach for future researches on paired topological states.
