光晶格中冷原子系统给人们研究关联量子体系、制备和研究新奇物质态提供一个重要的平台。我们计划研究：① 对于含有配对隧穿的玻色哈伯德系统，在三体限制下, 三角晶格中准硬核配对超固体到与其它相之间相变的普适类。 ② 在三体限制下，在立方晶格中能否找到硬核配对超固体，以及粒子-空位配对对硬核配对超固体形成机制的影响。③ 突破三体限制后，在二分的晶格（如一维，正方和六角晶格）中探索软核配对超固体的存在条件和特征。在本项目中，我们运用自行改进的量子蒙特卡罗算法模拟含配对隧穿的玻色哈伯德模型, 并将结果和平均场理论进行对比。我们的结论有助于将Gutzwiller平均场理论运用到三角晶格中玻色哈伯德问题, 而且有助于理解超固体存在的机制(搀杂或空位凝聚, 有序无序, 无搀杂)。

Cold atom in optical lattice provides us an important platform to study correlated quantum system and prepare new states of matter for research. We aim to study：① the university of phase transitions between pair supersolid and other phases of Bose-Hubbard model with boson pair tunneling under three-body constraint on the triangular lattice, ② the existing condition for the quasi-hardcore pair supersolid on cubic lattice and the effects of particle-hole pairs on supersolid. ③ the properties of softcore pair supersolid onbipartite lattice( one –dimensional chain, square lattice and honeycomb lattice). In this project, we prepare to simulate the Bose-Hubbard model with pair tunneling term by our sef-improved Quantum Monte Carlo method and comparing the results with Gutzwiller mean-field method. The results are helpful to apply the Gutzwiller mean-field theroy to solve extended Bose-Hubbard model on the triangular lattice and understanding the mechanisms of supersolid(doped defect condensation, order by disorder, without doping ).