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 Z2 × Z3.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.
frustrated magnetssuperfluidmott insulatordensity wave ordered phaseclock model
Ce Wang、Yu Chen
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School of Physics Science and Engineering,Tongji University,Shanghai,200092,China
Institute for Advanced Study,Tsinghua University,Beijing,100084,China
Graduate School of China Academy of Engineering Physics,Beijing,100193,China
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