在近年来研究基础上，我们将继续结合解析推导，尤其是非微扰的数值技术，集中探讨几何阻挫体系中电子关联驱动的磁性、超导电性及新颖量子态。当前，许多具有阻挫和电子关联特性的新材料被制备出来，如有机超导体、铁基超导体及掺杂石墨烯；同时，很多新奇物性或不容易研究清楚的奇异量子态在阻挫系统中产生，如量子自旋液体态等。在有效地考虑了各种相关晶格上的Hubbard（排斥相互作用）及其衍生模型的基础上，研究(1)阻挫对系统磁序的影响；(2)超导配对对称性在阻挫系统中的竞争及与磁序的关系；(3)阻挫的刻画；(4）量子自旋液态的实现等。通过这些研究，理解有机超导体中磁性和超导配对对称性的关系，解决铁基超导体中配对对称性与反铁磁序及其涨落等重要问题，探索二维六角晶格上的Hubbard模型等阻挫与电子关联驱动的非常规超导、量子自旋液体态等新物相。通过研究四种几何阻挫体系从无阻挫到全阻挫的过渡，寻找刻画阻挫的物理量。

Based on our recent research in related field, we should continue on studying the magnetism, superconductivity and novel quantum states driven by electronic correlation in geometrical frustrated system by using non-perturbative approaches and analytical method. Geometrical frustration appears in a wide variety of solid states and induces many novel and complex phenomena. Recent progress in material synthesize of geometrically frustrated systems put them into spot light again because many fascinating magnetic phenomena, such as ferromagnetism, superconductivity, and quantum spin liquid state, were observed or predicted. The results manifest a clearly important role played by the geometrical frustration hence call for understanding both the nature of frustration and electronic correlation in these materials. In this project, we plan to carry out a systematic study on the geometrically frustrated systems, and explore the nature of magnetism, superconductivity and novel quantum states in these systems. This is a difficult task because both quantum many-body effects and the Coulomb interaction needed to be treated properly, and one must deal with interplay of all interactions in order to capture physical properties correctly. We shall investigate the spin correlation and corresponding structure factor, and pairing correlation by performing extensive numerical calculations such as quantum Monte Carlo simulations and exact diagonalization studies, to determine the phase diagram and compared with structural and spectroscopic information obtained experimentally. These non-perturbative approaches are necessary to clarify some ambiguities and unresolved issues in some challenging novel materials. Specifically, we select four systems as sketched in page 7 to investigate. By varying hopping integral t1, we study the dominant magnetic order and superconductivity during the crossover (or transition) from a non-frustrated system to a fully-frustrated system. Moreover, based on our systemic studies on magnetic orders in different kinds of geometrically frustrated systems, we will try to identify a physical quantity the measure of the frustration. Our recent success in double triangular and honeycomb layers, as well as S4 model, put us in a promising start and our team is confident in completing the project successfully. Our findings will provide important information to condensed matter fields. For example, the investigation on the origin of ferromagnetism may lead to possible controllability of ferromagnetism in novel materials, and also promote the understanding on the superconductivity in Iron-based superconductivity, as well as the quantum spin liquid state in new geometrically frustrated systems.