Haldane-Shastry模型(H-S模型)是一种典型的、可积的长程相互作用模型，它和强关联系统、Yangian量子群等物理问题有着密切的联系。我们将借助拓扑基实现，构造并研究有意义的扩展的H-S模型，进而揭示二体、三体和四体等互作用的强弱分别对整体系统的物理性质的影响；描述其相应的拓扑性质，并进一步揭示拓扑基在此模型中具有的特殊物理性质。研究思路为：区分近邻和次近邻等互作用，由相应的Temperley-Lieb代数的生成元构造出H-S模型的哈密顿量族，进而使拓扑基成为哈密顿量族的共同本征态。在此基础上，思考扩展的H-S模型，也就是由哈密顿量族组合一个新的哈密顿量：同时包含二体、三体和四体等互作用，进而研究其相应的物理应用，并进一步讨论其能量基态和拓扑基态之间的对应关系。我们还将研究系统的几何相位和量子纠缠等物理问题

Haldane-Shastry model(H-S model), which is closely connected with strongly correlated systems and Yangian quantum groups, is one kind of typical.and integrable long-ranged interaction models. In this work, based on the spin realization of topological basis, we will construct and study a meaningful and extended H-S model for the purpose of finding the influences of two spins interaction, three spins interaction and four spins interaction on the physical applications of the whole system, describing its topological properties, and then revealing the particular physical properties of the topological basis in this system. The train of thought is that distinguishing the nearest and next-to-nearest neighbour interaction, the Hamiltonians family of the H-S model can be constructed from the corresponding Temperley-Lieb algebra generator, and then the topological basis states become the common eigenstates of the Hamiltonians family. Based on the above study, we will consider a extended H-S model, whose Hamiltonian, containing two spins interaction, three spins interaction and four spins interaction, will be combined by the Hamiltonians family of the H-S model. In the following, we will study the corresponding physical applications of the system. And then the relationship between the ground states of the system and the topological basis states will be discussed. Furthermore, we will investigate the geometric phase and quantum entanglement of the system, etc.