Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study*

Motivated by the realization of Bose-Einstein condensates (BEC) in non-cubic lattices, in this work we study the phases and collective excitation of bosons with nearest neighbor interaction in a triangular lattice at finite temperature, using mean field (MF) and cluster mean field (CMF) theory. We compute the finite temperature phase diagram both for hardcore and softcore bosons, as well as analyze the effect of correlation arising due to lattice frustration and interaction systematically using the CMF method. A semi-analytic estimate of the transition temperatures between different phases is derived within the framework of MF Landau theory, particularly for hardcore bosons. Apart from the usual phases such as density waves (DW) and superfluid (SF), we also characterize different supersolids (SS). These phases and their transitions at finite temperatures are identified from the collective modes. The low lying excitations, particularly Goldstone and Higgs modes of the supersolid can be detected in the ongoing cold atom experiments.