中文摘要：

对称性自发破缺和费米液体理论作为凝聚态物理的两大基石是我们理解凝聚态物质的结构、物性、相变的出发点．在强关联电子系统中，电子关联效应有可能导致超越对称性自发破缺的新的有序形式和与之相应的新的元激发形式．这些新的有序形式往往与量子力学特有的非局域性相关，并伴随着低能规范自由度的涌现．为此，有必要扩展传统的朗道理论范式，使我们对物质结构的认识提升到量子波函数的层次．

英文摘要：

The Landau theory of phase and phase transition, which describes the state of matter by the spontaneous symmetry breaking, and the Fermi liquid theory of interacting Fermi systems are the two corner stones of contemporary condensed matter physics. They act as our starting points to understand the structure, excitations and phase transitions of any condensed matter system. According to such a Landau paradigm, an interacting Fermi system will behave just as non-interacting Fermi gas system at sufficient low energy, if the interaction is not strong enough to induce a symmetry breaking phase transition in the system. In such a case, the perturbation expansion in the interaction strength is assumed to converge and the low energy excitation can be connected to that of a Fermi gas system adiabatically. In strongly correlated electron systems, such as the high temperature superconductors and quantum antiferromagnets, a pertubative picture on the interaction effect usually fails. The correlation effect between the electrons can induce new forms of order that are beyond the Landau symmetry breaking paradigm. Non-Fermi liquid behavior can emerge in the fully symmetric correlated phases. The Mott insulating phase and the quantum spin liquid phase are the most prominent example of such exotic state of matter. After about three decades of intensive studies, people find that the quantum non-locality effect is at the heart of such new forms of order. The quantum non-locality effect manifests itself in the emergence of gauge degree of freedom in the low energy physics of such strongly correlated system. Such emergent gauge filed is not only important for the characterization and classification of the ground state structure, but is also directly responsible for the non-Fermi liquid behavior of the system. The Landau paradigm should be extended to accommodate such new forms of order and the related new form of excitations and new universal class of phase transitions. Such an extension will elevate our understanding of the structure