By using slave particle (slave boson and slave fermion) techniques on the Bose-Hubbard model, we study the finite temperature properties of ultracold Bose gases in optical lattices. The phase diagrams at finite temperature are depicted by including different types of slave particles and the effect of the finite types of slave particles is estimated. The superfluid density is evaluated using the Landau second order phase transition theory. The atom density, excitation spectrum, and dispersion curve are also computed at various temperatures, and how the Mott-insulator evolves as the temperature increases is demonstrated. For most quantities to be calculated, we find that there are no qualitative differences in using the slave boson or the slave fermion approaches. However, when studying the stability of the mean field state, we find that in contrast to the slave fermion approach, the slave boson mean field state is not stable. Although the slave boson mean field theory gives a qualitatively correct phase boundary, it corresponds to a local maximum of Landau free energy and cannot describe the second order phase transition because the coefficient a(4) of the fourth order term is always negative in the free energy expansion.

中文翻译：

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光学晶格中超冷玻色气体有限温度特性的从属粒子方法

通过在 Bose-Hubbard 模型上使用从粒子（从玻色子和从费米子）技术，我们研究了超冷玻色气体在光学晶格中的有限温度特性。通过包括不同类型的从属粒子来描述有限温度下的相图，并估计有限类型的从属粒子的影响。使用朗道二阶相变理论评估超流体密度。还计算了不同温度下的原子密度、激发光谱和色散曲线，并演示了莫特绝缘体如何随着温度的升高而演变。对于大多数要计算的量，我们发现使用从玻色子或从费米子方法没有质量差异。然而，在研究平均场状态的稳定性时，我们发现，与从费米子方法相比，从玻色子平均场状态不稳定。虽然从玻色子平均场理论给出了一个定性正确的相界，但它对应于朗道自由能的局部最大值，并且不能描述二阶相变，因为四阶项的系数 a(4) 在自由能中始终为负能量膨胀。