Recent theoretical works have demonstrated the realization of fractional
quantum anomalous Hall states (also called fractional Chern insulators) in
topological flat band lattice models without an external magnetic field. Such
newly proposed lattice systems play a vital role to obtain a large class of
fractional topological phases. Here we report the exact numerical studies of
edge excitations for such systems in a disk geometry loaded with hard-core
bosons, which will serve as a more viable experimental probe for such
topologically ordered states. We find convincing numerical evidence of a series
of edge excitations characterized by the chiral Luttinger liquid theory for the
bosonic fractional Chern insulators in both the honeycomb disk Haldane model
and the kagom\'{e}-lattice disk model. We further verify these current-carrying
chiral edge states by inserting a central flux to test their compressibility.Comment: 5 pages, 4 figures, 1 table, with Supplementary Materia
