近些年来，量子自旋液体成为了物理学的研究热点。其中，Kitaev自旋模型，由于其基态为量子自旋液体并且模型具有难得的严格可解性，引起了广泛的兴趣。为了实现Kitaev自旋液体，实验上发现了一系列Kitaev材料，但基态多为磁有序态。这些磁有序态和其外场诱导下的磁无序态与Kitaev自旋液体的关系是一个开放性问题。本项目将以Kitaev材料的有效模型为研究对象，开展对Kitaev自旋液体态的研究。具体研究内容包括，在强关联电子模型的框架下，研究模型在自由电子极限下与强关联极限下拓扑性质的联系；研究Kitaev自旋液体在其他自旋相互作用与外场下的稳定性，确认Kitaev材料中的不同相与Kitaev自旋液体相的关系；根据以上结果，尝试给出简单的有效场理论解释其中的相变机制，并解释实验现象。该研究丰富了量子自旋液体的研究内涵，为探索可能实现Kitaev自旋液体的新型Kitaev材料提供理论依据。

Exploring exotic quantum phases and phase transitions is one of the frontiers of physics. Recently, quantum spin liquids, viewed as topological orders, which beyond the conventional paradigm attract great attention. Kitaev Honeycomb lattice model arouse wide interests since its ground state is rarely analytical solvable to be quantum spin liquids. Though its peculiar spin interactions seem rather unrealistic, it was shown that some spin-orbit Mott insulators can potentially realize some variants of this model and the corresponding materials are called Kitaev materials. It is found that the ground states are almost magnetically ordered, but the relations between the magnetically ordered ground states or the field-induced magnetically disordered states and Kitaev spin liquids are open questions. In this project, focusing on the effective model of Kitaev materials, we will study the Kitaev spin liquids based on the experimental consequences. Firstly, we attend to study the relation between the topological properties in the free electron limit and the strongly correlated limit. Then we will discuss the stability of Kitaev spin liquids and identify the relations of different phases to Kitaev spin liquids. Finally, on these bases, we will apply an effective field theory to understand the phase transitions and explain the experimental phenomena. The results would contribute to the studies of quantum spin liquids and realization of Kitaev spin liquids.