RUI: Theoretical (Numerical) Investigations of Novel Quantum Phases and Transitions in Strongly Interacting Systems

非技术摘要该 RUI 奖项支持计算和理论研究以及教育，以研究材料中电子之间相互作用强烈的不寻常物理特性。在这些材料中，量子力学发挥着重要作用，它们的磁性通常由电子固有磁性方向形成的模式决定。越来越多的磁性材料实验发现刺激了这一领域的研究，这些材料表现出与已知形式的磁性不同的不寻常特性。 PI 将使用计算机模拟和理论来研究新型磁性形式的基本性质，其中一些受挫磁体材料的启发，其中磁序最小基本单元之间的相互作用由于其在材料中的几何排列而无法满足。目的是预测这些材料关于磁性基本单位模式的定性行为，并测量量子力学如何将彼此相距甚远的基本磁性单位交织在一起。对这些相互作用系统的复杂特性的更好的理解和定量预测将为此类系统的分析理论和实验研究的发展提供信息和指导。更好地了解这些材料有助于为未来的设备技术建立知识库，这些技术的运行依赖于量子力学的基本原理，包括量子计算机。该研究将与本科生和研究生的教育相结合。该项目将为学生和博士后研究员提供解决挑战性问题和在凝聚态物理前沿开展研究的培训。它还将为少数族裔和第一代学生做好准备和培训，让他们为继续攻读博士学位时将面临的挑战做好准备。非技术摘要该 RUI 奖支持理论研究和教育活动，以研究受挫磁性材料和掺杂莫特绝缘体系统中新兴量子自旋液体、自旋玻色金属和非费米液体的基本性质。最近发现的磁性材料的不寻常的实验性质，包括赫伯特铁戈梅自旋系统和三角形有机化合物，成为这项研究的动力。这些系统表现出了可能的自旋液体或非费米液体的性质。 PI 计划研究微观系统中的量子相图和带隙自旋液体的拓扑性质，这些系统可能出现在 kagome 和其他具有几何挫败和竞争相互作用的晶格系统中。将开发一种系统方法，可以访问不同的拓扑扇区，获得纠缠信息和模矩阵，以充分表征量子自旋液相的拓扑性质。将确定弱莫特绝缘体的量子相图，以确定与具有海森堡交换和环交换相互作用的有机化合物相关的可能的无间隙自旋液体或非费米液体。 PI将开发一种受控且无偏的数值方法来研究准一维系统中微观自旋和电子模型中的无间隙液相，并基于有限尺寸缩放分析缩放到二维。 PI还将系统地研究这些奇异的量子液态与其他磁有序或空间对称破缺态之间的量子相变的性质，以寻找解禁量子临界性的特征。结合实验系统，系统地研究材料中额外的现实扰动的影响。作为其计算方法的核心，PI 和合作者将继续开发一种新的密度矩阵重整化群方法，该方法将为材料和超冷原子系统中的强相互作用系统找到广泛的应用。该研究的目标是提高对这些相互作用系统中新兴量子相的基本性质的理论理解，并为未来的理论和实验研究提供基于数值建模的定量预测和基准结果。与这项工作相一致，PI希望开发新的方法和工具，为材料和超冷原子系统中的强相互作用系统找到广泛的应用。通过进一步开发PI的密度矩阵重整化群算法，并结合矩阵乘积态和张量网络重整化，将探索这些受挫磁性和掺杂莫特绝缘体系统中令人兴奋的物理现象。该研究将与本科生和研究生的教育相结合。该项目将为学生和博士后研究员提供解决挑战性问题和在凝聚态物理前沿开展研究的培训。它还将为少数族裔和第一代学生做好准备和培训，让他们为继续攻读博士学位时将面临的挑战做好准备。在物理学或其他科学领域。

NONTECHNICAL SUMMARYThis RUI award supports computational and theoretical research, and education to investigate the unusual physical properties of electrons in materials that interact strongly with each other. In these materials, quantum mechanics plays a significant role and their magnetic properties are often determined by the patterns formed by the orientations of the intrinsic magnetism of the electrons. The research in this area is stimulated by growing experimental discoveries of magnetic materials which have exhibited unusual properties different from known forms of magnetism. The PI will use computer simulation and theory to study the fundamental nature of novel forms of magnetism, some inspired by materials known as frustrated magnets in which the interactions among the smallest fundamental units of magnetic order cannot be satisfied because of their geometric arrangement in the material. The aim is to predict the qualitative behavior of these materials regarding the pattern of the fundamental units of magnetism and measures of how quantum mechanics intertwines fundamental magnetic units that may be widely separated from each other. The improved understanding and quantitative prediction of the complex properties of these interacting systems will provide information and guidance for the development of analytic theories and experimental research on such systems. A better understanding of these materials contributes to the knowledge base for future device technologies based that relay on the fundamental principles of quantum mechanics for their operation, including quantum computers. The research will be integrated with the education of undergraduate and graduate students. The project will provide students and postdoctoral fellows with training in solving challenging problems and in carrying out research at the forefront of condensed matter physics. It will also prepare and train minority and first generation students to be ready for the challenges they will face when they go on to their graduate study for the Ph.D. in physics or other science.NONTECHNICAL SUMMARYThis RUI award supports theoretical research and education activities to investigate the fundamental nature of emerging quantum spin liquids, spin Bose metals, and non-Fermi liquids in frustrated magnetic materials and doped Mott insulator systems. The recent discoveries of unusual experimental properties of magnetic materials including Herbertsmithite kagome spin systems and triangular organic compounds serve as the impetus for this research. These systems have exhibited properties of possible spin liquids or non-Fermi liquids. The PI plans to study quantum phase diagrams and the topological nature of the gapped spin liquid in microscopic systems which may emerge in kagome and other lattice systems with geometric frustration and competing interactions. A systematic approach will be developed which can access different topological sectors, obtain entanglement information and the modular matrix to fully characterize the topological nature of the quantum spin liquid phase. The quantum phase diagram of a weak Mott insulator will be determined to identify the possible gapless spin liquid or non-Fermi liquid relevant for the organic compounds with Heisenberg exchange and ring-exchange interactions. The PI will develop a controlled and unbiased numerical approach to study gapless liquid phases in microscopic spin and electron models in quasi one-dimensional systems and scale to two-dimensions based on finite-size scaling analysis. The PI will also systematically study the nature of quantum phase transitions between these exotic quantum liquid states and other magnetically ordered or spatial symmetry broken states to search for the signature of a deconfined quantum criticality. In connection with experimental systems, the effect of additional realistic perturbations in materials will be systematically studied. Central to their computational approach, the PI and collaborators will continue developing a new density matrix renormalization group method that will find extensive applications for strongly interacting systems in both materials and ultra cold atom systesms. The objectives of the research are to improve the theoretical understanding of the fundamental nature of new emerging quantum phases in these interacting systems, and to provide quantitative predictions and benchmark results based on numerical modelling for future theoretical and experimental studies.In concert with this effort the PI hopes to develop new approaches and tools that will find extensive applications for strongly interacting systems in both materials and ultra cold atom systems. By further developing the PI's density matrix renormalization group algorithm, and incorporating matrix product states and tensor network renormalization, the exciting physics in these frustrated magnetic and doped Mott-insulator systems will be explored.The research will be integrated with the education of undergraduate and graduate students. The project will provide students and postdoctoral fellows with training in solving challenging problems and in carrying out research at the forefront of condensed matter physics. It will also prepare and train minority and first generation students to be ready for the challenges they will face when they go on to their graduate study for the Ph.D. in physics or other science.