Solving quantum impurity problems may advance our understanding of strongly correlated electron physics, but its development in multi-impurity systems has been greatly hindered due to the presence of shared bath. Here, we propose a general operation strategy to disentangle the shared bath into multiple auxiliary baths and relate the problem to a spectral decomposition problem of function matrix for applying the numerical renormalization group (NRG). We prove exactly that such decomposition is possible for models satisfying (block) circulant symmetry, and show how to construct the auxiliary baths for arbitrary impurity configuration by mapping its graph structure to the subgraph of a regular impurity configuration. We further propose an approximate decomposition algorithm to reduce the number of auxiliary baths and save the computational workload. Our work reveals a deep connection between quantum impurity problems and the graph theory, and provides a general scheme to extend the NRG applications for realistic multi-impurity systems.

翻译：求解量子杂质问题可能推进我们对强关联电子物理的理解，但由于共享库的存在，多杂质体系中的相关发展受到极大阻碍。本文提出一种通用操作策略，将共享库解缠为多个辅助库，并将该问题归结为函数矩阵的谱分解问题，从而应用数值重整化群（NRG）方法。我们严格证明了该分解对于满足（分块）循环对称性的模型是可行的，并通过将杂质配置的图结构映射到规则杂质配置的子图，展示了如何为任意杂质构型构造辅助库。进一步地，我们提出了一种近似分解算法，以减少辅助库数量并节省计算开销。本研究揭示了量子杂质问题与图论之间的深层联系，并为将NRG方法拓展至实际多杂质体系提供了通用方案。