  We consider the extended hard-core Bose-Hubbard model on a Kagome lattice
with boundary conditions on two edges. We find that the sharp edges lift the
degeneracy and freeze the system into a striped order at 1/3 and 2/3 filling
for zero hopping. At small hopping strengths, holes spontaneously appear and
separate into fractional charges which move to the edges of the system. This
leads to a novel edge liquid phase, which is characterized by fractional
charges near the edges and a finite edge compressibility but no superfluid
density. The compressibility is due to excitations on the edge which display a
chrial symmetry breaking that is reminiscent of the quantum Hall effect and
topological insulators. Large scale Monte Carlo simulations confirm the
analytical considerations.
