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

通过数值求解投影Gross-Pitaevskii方程，研究了具有限制势的准二维稀玻色气体系统的有限温度性质。相干区与非相干区交界处的相位关联函数的指数与KT相变的指数相同。我们还通过量子Monte Carlo模拟研究了正方形格子上的扩展硬核玻色-Hubbard模型的有序性。在这个系统中，化学势特别地沿x轴沿着增加。结果表明，棋盘格固态和超流态在hc处有很好的空间分离，粒子密度在hc处发生跳跃，hc对应于均匀势系统的一级相变临界值。当我们改变潜在的形状时，这种行为并没有改变。这表明，静态量，如颗粒密度，局部压缩性和局部刚度，可以解释的局部密度近似。

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.