量子杂质系统描述受限小量子系统与具有连续自由度的环境之间的相互作用，是凝聚态物理重要的研究方向之一。自从上世纪七十年代人们对Kondo效应的研究以来，量子杂质系统的研究对象和研究方法已经有了极大的扩展。在本研究计划中，我们针对当前量子杂质体系的若干热点和难点问题，提出运用数值重整化群(NRG)方法进行研究的具体方案和可行性分析。数值重整化群方法是研究量子杂质模型的有力工具之一。本研究计划包括四个方面的内容：（1）自旋－玻色子系统的NRG研究；（2）石墨稀中量子杂质效应的NRG研究；（3）多轨道Kondo问题的NRG研究；以及（4）NRG方法的发展。对每一部分研究内容，我们详细描述了选题的物理背景、课题的科学意义，拟解决的关键问题，并详细阐述了具体的研究方案和可行性。

Quantum impurity systems describe a confined small quantum system interacting with continuous environmental degrees of freedom. It is one of the important research areas in the condensed matter physics. Since the research of Kondo problem in 1970's, the research object and the methodology have been extended greatly. In this research plan, aiming at several hot and difficult physical problems in the area of quantum impurity systems, we plan to use the numerical renormalization group (NRG) method to study these problems and we analyze the feasibility of these proposals. NRG is one of the most powerful methods that have been used to study quantum impurity models. Our proposal include 4 distinct projects: (1)NRG study of the spin-boson systems; (2) NRG study of the quantum impurities on graphene; (3)NRG study of the multi-orbital Kondo problem; and (4) Development of NRG method. For each project, we describe the physical background, its scientfic significance, and the key problem to be solved. We also present detailed research procedure and analyze its feasibility.