量子自旋液体的研究一直是最近几十年凝聚态物理学界的研究热点。其中，量子自旋轨道液体在自旋基础上引入轨道自由度而备受关注。近期有理论提出SU(4)对称量子自旋轨道液体可能在强自旋轨道耦合材料中实现。由于实际材料是复杂的，总是存在破坏高对称的作用项，因此量子自旋轨道液体的稳定性仍然是一个开放问题。本项目将以可能实现量子自旋轨道液体的候选材料为对象，寻找材料的低能有效模型；并在此基础上，讨论磁场以及破坏SU(4)对称的相互作用项对量子自旋轨道液体稳定性的影响;研究量子自旋轨道液体中的自旋、轨道激发以及单空穴（电子）的动力学问题，理解自旋、轨道与电荷自由度的关系。为实验上寻找量子自旋轨道液体提供理论依据，对充实量子自旋液体的研究内涵提供有价值的参考。

For decades, the research on the quantum spin liquids has been a major focus of the condensed matter physics. As one of quantum spin liquids, quantum spin-orbital liquids attract great attention due to the existence of spin and orbital degrees of freedom. Recently, it has been proposed that SU(4)-symmetric quantum spin-orbital liquid may be realized in materials with strong spin-orbital coupling. Since the real materials are intricate and host the perturbation terms which destroy the SU(4) symmetry, so the stability of quantum spin-orbital liquids in such materials is still open question. In this project, we will focus on these candidate materials and find a low-energy effective model. Based on the effective model, we intend to discuss the effect of the magnetic field and the SU(4)-symmetry-broken interaction terms on the stability of quantum spin-orbital liquid. Then, we will investigate the dynamics of spin, orbital, and single hole (electron) in quantum spin-orbital liquid to clarify the interplay between them. These results will provide valuable information for the enrichment of quantum spin liquid research and realization of quantum spin-orbital liquids.