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

该RUI奖支持计算和理论研究，以及调查相互作用强烈的材料中电子的不寻常物理性质的教育。在这些材料中，量子力学起着重要的作用，它们的磁性通常由电子的本征磁性方向形成的模式决定。这一领域的研究受到越来越多的磁性材料实验发现的刺激，这些材料表现出不同于已知形式的磁性的不寻常性质。PI将使用计算机模拟和理论来研究新型磁性的基本性质，其中一些灵感来自于被称为受挫磁铁的材料，在这种材料中，由于它们在材料中的几何排列，磁性秩序的最小基本单位之间的相互作用不能得到满足。其目的是预测这些材料关于磁性基本单位模式的定性行为，以及量子力学如何将相互分离的基本磁性单位缠结在一起的测量。提高对这些相互作用系统复杂性质的理解和定量预测，将为这些系统的分析理论和实验研究的发展提供信息和指导。更好地理解这些材料有助于建立基于量子力学基本原理的未来设备技术的知识库，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提供培训，以解决具有挑战性的问题，并在凝聚态物理的前沿开展研究。它还将准备和培训少数族裔和第一代学生，为他们在继续攻读物理或其他科学博士学位时将面临的挑战做好准备。该RUI奖支持理论研究和教育活动，以调查新兴量子自旋液体，自旋玻色金属和非费米液体在受挫磁性材料和掺杂莫特绝缘体系统中的基本性质。最近发现的磁性材料的不同寻常的实验性质，包括Herbertsmithite kagome自旋系统和三角形有机化合物，为这项研究提供了动力。这些体系表现出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可能出现在kagome和其他具有几何挫折和竞争相互作用的晶格系统中的量子相图和间隙自旋液体的拓扑性质。本文将开发一种系统的方法，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。确定弱莫特绝缘体的量子相图，以确定与海森堡交换和环交换相互作用相关的有机化合物可能存在的无间隙自旋液体或非费米液体。PI将开发一种可控和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量子液态和其他磁有序或空间对称破缺态之间的量子相变的本质，以寻找定义量子临界性的特征。结合实验系统，将系统地研究材料中附加的实际扰动的影响。作为计算方法的核心，PI和合作者将继续开发一种新的密度矩阵重整化群方法，该方法将广泛应用于材料和超冷原子系统中的强相互作用系统。研究的目的是提高对这些相互作用系统中新出现的量子相的基本性质的理论认识，并为未来的理论和实验研究提供基于数值模拟的定量预测和基准结果。为了配合这项工作，PI希望开发新的方法和工具，在材料和超冷原子系统的强相互作用系统中找到广泛的应用。通过进一步发展PI的密度矩阵重整化群算法，并结合矩阵积态和张量网络重整化，探索这些受挫磁和掺杂莫特绝缘子系统中的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提供培训，以解决具有挑战性的问题，并在凝聚态物理的前沿开展研究。它还将准备和培训少数族裔和第一代学生，为他们在继续攻读物理或其他科学博士学位时将面临的挑战做好准备。

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.