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 in noncubic lattices [J. Struck, Science 333, 996 (2011)10.1126/science.1207239], 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 analyze the effect of correlation arising due to geometric frustration of a triangular lattice and interaction systematically using the CMF method. A semianalytic 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 and superfluid, we also characterize different supersolids. These phases and their transitions at finite temperature 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.