Mott insulator-density ordered superfluid transition and ‘shamrock transition’ in a frustrated triangle lattice

Abstract

Abstract 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. Furthermore, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau–Ginzburg (LG) paradigm. A U(1) symmetry is emergent at the critical point, while the symmetry in each density ordered superfluid is Z 2 × Z 3. We call the transition a ‘shamrock transition’, due to its degenerate ground state in the parameter space being a shamrock-like curve rather than a circle in an LG-type transition. Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.