Competing scenarios for dipolar hard-core bosons within square and triangular lattices

Thanks to the fast development of cold-atom experiments, an exotic quantum phase with coexisting solid(diagonal) and superfluid(off-diagonal) long-range orders, also named after the supersolid state, has been realized. This quantum phase was discovered within a trapped Bose-Einstein condensate made of dipolar atomic gases. Within a planer lattice, such dipolar interaction can be easily tuned by varying the external field, and thus remains flexible for creating distinct scenarios. In our recent works, we have found a competing scenario between phases belonging to different lattice symmetry, among the variation of dipolar angles. Based on the preliminary mean-field analysis, we further made use of numerical techniques and provided more insightful features of the phase diagrams. Experimentally, we believe that the tuning of dipolar interaction helps change the geometrical structure of the lattice and realize an effective reciprocal structure.