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

技术总结该奖项支持对相互作用的玻色子和自旋系统进行广泛的计算研究，这对理解强关联多体物理至关重要。这项研究的目的是从根本上洞察被困在光学晶格和受挫磁场中的超冷原子可能实现的功能。PI旨在研究三角形和其他晶格系统上具有受阻跳跃和长程斥力的玻色子-哈伯德模型，以了解实现新量子相的微观条件，包括不同的超固态相、Mott绝缘体和可能的自旋-液体相。这样的研究可以定量地预测相互作用玻色子系统的整体相图，并揭示量子相变的性质，它可能属于一个新的普适类。PI还将研究强关联和受阻磁系统中的自旋液体行为、分馏化、拓扑有序和相关的量子相变。通过实验发现了越来越多的磁性材料，它们呈现出候选的自旋-液体状态。PI将结合精确的Lanczos方法和密度矩阵重整化群方法来研究各种量子自旋模型中的低能谱、拓扑简并和自旋-自旋关联函数。PI的目的是获得基本的见解，这项研究可能会建立？原则性证明？在Kagome和正方形晶格上的简单自旋模型中存在新的自旋液体相的证据，旨在与关于钠钛铁矿和某些层状钒氧化物和复杂的钒磷酸盐的实验相联系。该项目支持学生和博士后研究人员的教育体验；少数民族学生将参与其中。这项研究为多体物理非技术性总结的新计算课程做出了贡献该奖项支持使用先进的计算技术来寻找新的物质电子态的计算研究和教育。PI将研究材料的模型，在这些材料中，最小的磁性单位不能简单地排列成磁铁或反铁磁体。相邻的最小磁性单位之间的相互作用不能通过任何排列在晶格上得到满足。这些受挫的磁铁是展示电子物质新状态的候选者。PI的目标是使用计算来确定特定的理论上提出的物质状态是否存在于被认为与候选材料相关的模型中，例如矿物钠锰矿和高温超导体。这是一项基础性研究，有助于我们理解材料和新的物质电子态的智力基础，这些物质表现出我们目前理解之外的性质和奇异现象。这本身就是一种智力追求，不亚于对宇宙的研究，但它也可能导致新现象的发现，并为未来的设备技术做出贡献。该项目支持学生和博士后研究人员的教育体验；少数族裔学生将参与其中。这项研究为新的多体物理计算课程做出了贡献

TECHNICAL SUMMARYThis award supports research involving an extensive computational study of interacting boson and spin systems which are of fundamental importance in understanding strongly correlated many-body physics. The research aims for fundamental insights into that may be realized in ultracold atoms trapped in optical lattices and frustrated magnets.The PI aims to study boson Hubbard models with frustrated hopping and long range repulsions on triangular and other lattice systems to understand the microscopic conditions for realizing new quantum phases including different supersolid phases, a Mott-insulator, and possible spin-liquid phases. Such an investigation can result in quantitative predictions for the global phase diagram of interacting boson systems and reveal the nature of the quantum phase transitions which may belong to a new universality class. The PI will also study the spin liquid behavior, fractionalization, topological order and related quantum phase transitions in strongly correlated and frustrated magnetic systems. There are a growing number of magnetic materials discovered by experiment which exhibit candidate spin-liquid states. The PI will combine the exact Lanczos method with density matrix renormalization group methods to study the low energy spectrum, topological degeneracy, and spin-spin correlation function in various quantum spin models. The PI aims to gain fundamental insights and the research may establish ?proof of principle? evidence for the existence of novel spin liquid phases in simple spin models on kagome and square lattices aiming to make contact with experiments on Herbertsmithite and certain layered vanadium oxides and complex vanadium phosphates. This project supports educational experiences for students and postdoctoral researchers; minority students will be involved. The research contributes to a new computational course on many-body physics NON-TECHNICAL SUMMARYThis award supports computational research and education that will use advanced computational techniques to search for new electronic states of matter. The PI will study models for materials in which the smallest units of magnetism cannot simply align in such a way to become a magnet or an antiferromagnet. The interactions between neighboring smallest units of magnetism cannot be satisfied on the crystal lattice by any alignment. These frustrated magnets are candidates to exhibit new states of electronic matter. The PI aims to use computation to see whether specific theoretically proposed states of matter exist in models that are believed to be relevant to candidate materials, for example the mineral Herbertsmithite and high temperature superconductors.This is fundamental research that contributes to the intellectual foundations of our understanding of materials and new electronic states of matter that exhibit properties and exotic phenomena that lie outside our current understanding. This is an intellectual pursuit in its own right no less fascinating than the study of the universe, but it may also lead to the discovery of new phenomena and to contribute to future device technologies.This project supports educational experiences for students and postdoctoral researchers; minority students will be involved. The research contributes to a new computational course on many-body physics