中文摘要：

通过综合模式搜索法、广义Lagrange乘子法、以及转轴法等多种数值方法,建立了一套针对多轨道Hubbard模型隶玻色子解法的数值优化方法.该数值方法能够在考虑晶场劈裂、轨道间跳跃以及真实能带结构基础上,利用隶玻色子方法计算实际关联电子材料的性质.首先利用该方法计算了两轨道体系的.Mott金属一绝缘体转变性质,得到了与目前已有工作一致的结果;然后利用该方法讨论了Coulomb关联对三轨道体系Na_xCoO_2的影响.结果表明：在中间关联情况下由eg轨道形成的六个小Fermi面消失,原因是由于电子关联导致该轨道上的空穴数随U减少.这些结果也证实了算法的正确性和有效性.

英文摘要：

A numerical algorithm is proposed for multi-orbital slave-boson mean field approach through the integrating pattern search method,the generalized Lagrange multiplier method,and the Rosenbrock method.Since the crystal field splitting,inter-orbital hopping and realistic band structures can be considered,the proposed slave-boson mean field approach can be utilized to study realistic material. To validate our algorithm,the Mott transitions in twoorbital Hubbard models are studied with the elliptical density of states.The results are consistent with the reported ones available.Then we use this method to study the correlation effect on the three-orbital Hubbard model for Na_xCoO_2.It is shown that the six small Fermi surfaces constructed by the e＇_g orbital vanish in the intermediate Coulomb correlations.The physical reason is that the hole occupations of e＇ orbital decrease with U increasing.All the calculated results verify the accuracy and the efficiency of our numerical algorithm.