确定电子关联体系中量子临界、超导电性、非费米液体行为等物理现象之间的内在关联，必须处理好电子关联效应；这是现代凝聚态物理理论的重点和难点，也是当前非常规超导研究遭遇到的“瓶颈”。2018年3月，实验报道魔转角双层石墨烯中，由于电子“平带”上表现出的强电子关联效应，导致了新颖的莫特绝缘相和超导相，与非常规超导体系有类似的相图；这为理论研究电子关联体系提供了崭新的理想平台：使用非微扰数值技术，准确描述电子关联体系的量子临界行为和超导电性。基于并发展现有量子蒙特卡罗方法，申请人拟探讨新颖“平带”电子关联体系量子临界点附近磁性和超导电性的竞争、无序、应力等驱动的新颖量子态等。这些体系包括双层转角六角晶格、Lieb晶格及Kagome晶格等，与石墨烯、铜氧化物高温超导以及拓扑材料密切相关；这些研究有助于建立一套能统一描述非常规超导机制的微观机制，并对新材料的实际应用提出新的物理机制。

To determine the intrinsic relationship between quantum critical, superconducting, non-Fermi liquid behavior and other physical phenomena in the electronic correlated system, it is necessary to deal with the electronic correlation; this is the focus and difficulty of modern condensed matter physics theory, and it is also the "bottleneck" encountered in superconducting research. Since March of 2018, the experimental works reported twisted-bilayer graphene has encountered a novel Mott insulation phase and superconducting phase, and unconventional superconductivity induced by the strong electronic correlation due to the "flat band". The system has a similar phase diagram as that of doped cuprates, and it provides a new ideal platform for the theoretical study of electronic correlated systems: using non-perturbative numerical techniques to accurately describe the quantum critical behavior and superconductivity of electronic correlated systems. By developing the state- of-art quantum Monte Carlo method, we intend to explore the novel quantum states driven by the competition between magnetism and superconductivity near the quantum critical point of the novel "flat band" electronic correlated system. These systems include twisted bilayer honeycomb lattices, Lieb lattices, and Kagome lattices, which are closely related to graphene, doped cuprates, and topological materials; these studies shall be helpful to establish a uniform description of unconventional superconductivity, and also to explore the new physical mechanism for the practical application of new materials.