Topological and critical states of matter in strongly correlated electronic systems

物质的拓扑和临界态具有根本的重要性，可能对未来的量子技术产生巨大的影响。这些新的物质状态是纯量子的，与属于经典对称性破缺范式的传统物质状态截然不同。近年来，我们目睹了这些新态理论的巨大发展。然而，该领域仍面临两大挑战：（1）在真实的材料中实现相互作用拓扑相;（2）理解物质临界态的精确性质。这些问题在本质上相互作用很强，而且不受干扰，这对社区使用传统方法解决这些问题构成了困难的障碍。我的研究目标是通过采用非微扰数值和量子场论分析来解决这两个挑战。 物质的拓扑态和临界态具有许多新的性质。例如，量子自旋液体表现出一种奇特的现象，称为自旋-电荷分离，其中电子被分成两个粒子，即自旋子和电荷。自旋子携带自旋为1/2的电荷，而电荷子携带一个电荷，没有任何自旋。这种新的性质可能有重要的应用，如拓扑量子计算和理解高温超导体。我的研究计划将使用数值方法（DMRG，Monte Carlo）和解析量子场论分析来研究自旋液体和其他强关联系统的理论。我的研究计划将在抽象理论和真实的实验之间建立一座桥梁，它也将连接物理学的不同领域。这项研究将使凝聚态系统成为研究有趣的量子场论的桌面实验平台，并将有助于解决凝聚态和高能物理中的未决问题。除了对基础科学的影响，我的研究也可能对技术产生影响，因为物质的新量子相对未来的量子技术至关重要。理解强相关材料可以为理解高温超导体铺平道路，并作为寻找室温超导体的指导。这可能会对未来的设备，运输和能源行业产生巨大的技术和实际影响。该研究还将有助于培养学生和研究人员具有先进的数值和理论技能。这两种技能的结合将使他们具有独特的优势，使他们能够为理论凝聚态物理学做出重要贡献。这些技能也将为材料科学和工业做好准备。例如，数值模拟和数据分析的技能将对金融和软件工程的职业有用。

Topological and critical states of matter are of fundamental importance and are likely to have a huge impact on the future quantum technology. These novel states of matter are purely quantum and are sharply distinct from conventional states of matter that fall in the classical symmetry breaking paradigm. In recent years, we have witnessed great developments in the theory of these novel states. However, there are still two major challenges in the community: (1) to realize interacting topological phases in real materials; (2) to understand the precise properties of critical states of matter. These problems are intrinsically strongly interacting and non-perturbative, which poses difficult obstacles for the community to solve them using conventional methods. The goals of my research are to tackle these two challenges by employing both non-perturbative numerics and quantum field theory analysis. Topological and critical states of matter have many novel properties. Quantum spin liquids, for example, exhibit an exotic phenomenon called spin-charge separation, in which the electrons are fractionalized into two particles, namely the spinon and chargon. The spinon is carrying spin-1/2 without any electric charge, while the chargon carries one electric charge without any spin. This novel property may have important applications, such as topological quantum computation and understanding high-temperature superconductors. My proposed research will study the theory of spin liquids and other strongly correlated system using numerical methods (DMRG, Monte Carlo) and analytical quantum field theory analysis. My research program will build a bridge between abstract theory and real experiments, and it will also connect different areas of physics. This research will enable condensed matter systems to be a table-top experimental platform to study interesting quantum field theories, and it will help to resolve open questions in both condensed matter and high energy physics. Besides the impact on fundamental science, my research will also likely to have an impact on technology, since novel quantum phases of matter will be critical for future quantum technology. Understanding strongly correlated materials can pave the way towards understanding high-temperature superconductors and serve as a guide in the search for a room temperature superconductor. This could have a large technological and practical impact on the devices, transportation, and energy industries of the future. The research will also contribute to training students and researchers with both advanced numerical and theoretical skills. The combination of these two skills will give them unique advantages, enabling them to make important contributions to theoretical condensed matter physics. These skills will also prepare them for material science and industry. For example, the skills of numerical simulations and data analysis will be useful for occupations in finance and software engineering.