一种求解Bose-Hubbard模型的简单方法  

A Simple Method to Solve the Bose-Hubbard Model

作　　者：张丹伟 

机构地区：[1]华南师范大学物理与电信工程学院,广州510006 [2]广东省量子调控工程与材料重点实验室,广州510006

出　　处：《四川理工学院学报（自然科学版）》2016年第4期74-77,共4页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：广东省自然科学基金项目(2016A030313436);广东省高校优秀青年创新人才培育项目(2015KQNCX023)

摘　　要：针对描述晶格中多体相互作用玻色子体系的Bose-Hubbard模型,首先计算相互作用能与跳跃能比值趋于无穷大和趋于零两种极限的基态,分别得到了莫特绝缘态和超流态两个量子相。其次利用平均场近似引入超流序参量,通过二阶微扰解析计算基态能量,从而得到体系从超流态到绝缘态的量子相变的边界方程。最后通过数值软件求解边界方程得到Bose-Hubbard模型的相图。该求解BoseHubbard模型的平均场方法不仅能够得到完整相图,而且整个过程物理图像清晰、简洁明了便于理解。For the Bose-Hubbard model that describes many-body interacting boson system in lattices,the ground states of the system when the ratios between the interaction and hopping energies tend to infinity and zero limits are respectively calculated. The Mott insulator and superfluid phases in these two cases are respectively obtained. Secondly,based on the meanfield approximation and the second-order perturbation method with the order parameter for the superfluid states,the groundstate energy of the system is calculated and then the boundary equation of the quantum phase transition from the superfluid state to the insulating state is obtained. Finally,the phase diagram of the Bose-Hubbard model is obtained by solving the phase boundary equation by using numerical software. This mean-field method for solving the Bose-Hubbard model is not only able to obtain the complete phase diagram,but also able to provide the concise physical figure which is clear in the whole process and easy to understand.

关 键 词：BOSE-HUBBARD模型 超流态 莫特绝缘态 平均场近似 相图 

分 类 号：O469[理学—凝聚态物理]