在研究磁性材料的时候，我们不可避免的要研究量子自旋系统。量子力学诞生不久，量子自旋系统就成为固体物理中非常活跃的研究领域。在过去的近百年的时间，人们用量子自旋模型成功解释或者预言了丰富的磁性现象。特别是，一些磁性材料中存在的阻挫，能极大的降低从高温无序相到低温有序相的转变温度，甚至这个转变会消失，即材料的基态是大家常说的量子自旋液体。对这类磁性材料和相关自旋模型的研究，能加深我们对一些新奇量子现象，如量子自旋液体、拓扑序、长程纠缠的理解，还能为我们寻找新型磁性材料提供帮助。在本课题中，我们拟利用密度矩阵重整化群、张量网络、严格对角化、以及 Monte Carlo 等数值算法结合一些解析的手段研究最近实验上发现的量子磁性材料和尚未解决的量子自旋模型；同时，我们将围绕强关联系统的研究，进一步改进和发展现有数值方法并将其应用到量子自旋系统的研究中，为这个领域的发展贡献我们的力量。

Soon after the discovery of quantum mechanics, the quantum spin systems became one of the active research areas in condensed matter physics, and in the past decades enormous materials associated with magnetism have been explored or predicted based on our understanding of the quantum spin systems. In particular, the frustration, which is ubiquitous in nature, can greatly reduce the transition temperature from paramagnetic phase to magnetically ordered phase. In some cases, this transition even does not occur, leading to so-called quantum spin liquid. These observations offer us insightful information to understand the long-sought quantum spin liquid, the topological order and the long-range entanglement, and may help us to synthesize new magnetic materials as well. In this project, we plan to study some quantum magnetic materials and quantum spin models by using the density-matrix renormalization group, tensor network, exact diagonalization, and Monte Carlo simulations in combination with some analytical treatments. Our work may deepen our understanding of these materials and models, and predict new experimental findings. Moreover, we may try to improve and develop numerical methods and apply them to study strongly correlated systems.