Motivated by the realization of Bose-Einstein condensates in noncubic lattices [J. Struck et al., Science 333, 996 (2011)], 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.

中文翻译：

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有限温度下三角形晶格中玻色子的相和集体模态：聚类平均场研究

非立方晶格中玻色-爱因斯坦凝聚的实现动机[J．Struck等。，科学 333，996（2011）]，在这项工作中，我们使用均值场（MF）和聚类均值场（CMF）理论研究了在有限温度下三角晶格中具有最邻近相互作用的玻色子的相位和集体激发。我们计算了硬核和软核玻色子的有限温度相图，并使用CMF方法分析了由于三角晶格的几何受挫和相互作用而引起的相关效应。在MF Landau理论的框架内，特别是对于硬核玻色子，得出了不同相之间转变温度的半解析估计。除了密度波和超流体等通常的相，我们还表征了不同的超固体。这些阶段及其在有限温度下的转变是从集体模式中识别出来的。