量子相以及量子相变的研究一直以来都是量子多体物理中重要课题之一。作为最成熟的量子模拟器，光晶格中的超冷原子系统成为了研究量子相变最为理想的平台。作为最具有代表性的莫特超流量子相变，对其解析方法的研究一直以来停留在定性的基础上。最近几年，课题组基于过程链方法开发了强耦合展开的高级微扰算法，将阶数提高到12阶，并首次将其符号运算化。本项目计划继续提升算法的通用性，将其拓展到各向异性的系统，并用于研究各向异性的玻色哈伯特模型中的相变问题。通过量子蒙特卡洛数值模拟方法辅助，研究维度过渡对于莫特态区域，莫特超流相变类型，临界指数以及超流密度分量的影响。本项目不仅填补了国内光晶格高级微扰论算法的空白，保证课题组在此方向的国际领先地位，同时也有助于深入理解维度过渡对于量子相变的影响。

Quantum phase and quantum phase transition are always important topics in the researches of quantum many-body physics. As the best quantum simulator, the system of the ultra-cold atoms in the optical lattice becomes the most ideal platform for studying the quantum phase transitions. As the most typical case, the Mott-superfluid phase transition can only be qualitatively analytically solved. Recently, we developed the high order strong coupling method basing on the process-chain approach with highest order 12, and we also symbolized it. In this project, we plan to extend the method to general case which can be used to solve the anisotropic Bose-Hubbard model. Accompanying with the quantum Monte Carlo simulations, we can study the effect of dimension crossover on the region of Mott phase, the universality class of Mott-superfluid phase transition and the superfluid density in different directions. This project not only fills the blank of the high order perturbation theory in the optical lattice system, but also help to deep understanding the effect of dimension crossover on the quantum phase transitions.