Orderings at a finite temperature in bosonic Hubbard model with confinement potentials

通过数值求解投影的Gross-Pitaevskii方程，研究了具有约束势的准2D稀玻色子气体系统的有限温度性质。相干区和非相干区交界处的位相关联函数的指数取与KT相变相同的值。我们还通过量子蒙特卡罗模拟研究了扩展的硬核玻色子-哈伯德模型在正方形晶格上的有序性。在这个体系中，化学势沿x轴特别增大。结果表明，棋盘状固体和超流态在Hc处有很好的分离，粒子密度在Hc处跳跃，Hc对应于均匀势能系统一阶相变的临界值。当我们改变可能的形状时，这一行为没有改变。这表明，粒子密度、局部可压缩性和局部刚度等静态量可以用局部密度近似来解释。

We investigated finite temperature properties of quasi-2D dilute-bosonic-gas system with confinement potential by numerically solving the projected Gross-Pitaevskii equation. The exponent of phase correlation functions at the boundary between coherent and in-coherent region takes the same values of the KT phase transition. We also studied the orderings of the extended hard-core bosonic-Hubbard model on the square lattice by performing the quantum Monte Carlo simulations. In this system, the chemical potential specially increases along the x-axis. The results indicated that the checker board solid state and superfluid state are well specially separated and the particle density jumps at hc, where hc corresponds to the critical values of the first order transition in the systems with uniform potential. This behavior was not changed when we changed the potential shapes. This suggests that the static quantities such as particle density, local compressibility, and local stiffness, can be explained by the local density approximation.