  Density order is usually a consequence of the competition between long-range
and short-range interactions. Here we report a density ordered superfluid
emergent from a homogeneous Mott insulator due to the competition between
frustrations and local interactions. This transition is found in a Bose-Hubbard
model on a frustrated triangle lattice with an extra pairing term. Further, we
find a quantum phase transition between two different density ordered
superfluids, which is beyond the Landau-Ginzburg paradigm. Across this
transition, a U(1) symmetry is emergent, while the symmetry in each density
ordered superfluid is Z2*Z3. Because there emerges a shamrock-like degenerate
ground state in parameter space, we call the transition "shamrock transition".
Effective low energy theories are established for the two transitions mentioned
above and we find their resemblance and differences with clock models.
