Simulation studies of ground state phases and criticality in correlated quantum matter

该奖项支持材料中电子物质新状态的理论研究和教育。材料的性质来自于它们的微观结构单元：原子和分子，特别是我们通常想象的围绕原子核旋转的电子。在金属中，一小部分电子从单个原子中分离出来，并在系统中迁移，而在其他材料中，所有电子都保持局部化。在任何一种情况下，电子都赋予了材料在电子元件和其他技术应用中所利用的电和磁特性。该项目旨在增加我们对电子由于相互作用而形成丰富的不同复杂状态的方式的理解。相互作用取决于承载电子的特定材料。作为微观粒子，电子的运动和相互作用受量子力学控制，构建易于处理的理论模型来描述它们，并理解和调整它们的特性在技术上具有挑战性。 在这个项目中，相互作用的电子模型的相关条件下，例如，高温超导材料形成的氧化铜层相互分离的其他原子。在这些材料中，电子形成了一种新的物质状态，即超导性，它可以在氧气为液体的温度下无损耗或电阻地导电。使用大规模的计算机模拟的模型进行了研究。该项目的核心是了解当模型参数（例如描述电子相互作用的参数）改变时，绝缘磁体如何转变为新的磁状态，以及注入这种状态的额外电子如何表现。理解这个模型系统可能是理解这些材料中超导性的物理起源的关键，并且可能为发现在更高温度下表现出超导性的新材料提供关键，为低损耗电力传输和新型电子设备等技术应用开辟道路。 除了科学意义外，该项目还旨在培养研究生在最先进的物理建模和计算机模拟方面的能力，并帮助开发用户友好的软件，以供其他研究人员应用所开发的方法和模型。技术总结该奖项支持材料中电子物质新状态的理论研究和教育。凝聚态物理学的一个重要方面是研究强关联量子物质系统的基态和激发，例如，高度受挫的量子磁体的局域自旋或铜氧化物高温超导体的价电子。 量子场论的描述通常包含涌现的成分，如自旋子、合子和规范场，它们是在唯象学和对称性论证的基础上提出的。场论通常只能在一定的极限下解。这项研究的重点是利用数值精确的量子蒙特卡罗技术来研究微观哈密顿算子，它可以被调整到各种制度，在这些制度中，通过研究低能物理可以检测到出现的粒子和场。这些研究可以与场论的结果，也可以产生实验检测的非常规集体电子态的签名。因此，这项研究可以连接晶格尺度物理和涌现低能行为，对相关量子物质的理论和实验研究产生潜在影响。 PI将研究J-Q模型，其中2D量子反铁磁体的磁有序基态可以被破坏，导致量子相变到非磁性状态，并形成价键固体。这些模型似乎拥有非常规的低能量子物体，可以解释为自旋和U（1）规范场。PI将解决这些粒子和场如何从晶格尺度出现到大的长度尺度，这些尺度可以通过为模型量身定制的强大模拟技术来访问。主要目标是：（i）将J-Q模型的激发与规范场理论联系起来，特别是探索在接近反铁磁体与价键固体之间的量子相变的系统中希格斯机制和希格斯玻色子的类比。(ii)引入移动的电荷载流子，这可能会导致holon，并探索与铜氧化物高温超导体的“奇怪金属”状态的联系。 作为该项目的一个组成部分，将开发新的和改进的模拟算法，这些算法在凝聚态物理学以及量子信息研究中感兴趣的超冷原子凝聚体和系统的研究中具有广泛的应用。这些模型和方法在高能粒子物理学中也很有意义，提供了一个比标准格点规范场理论更简单的环境来研究非微扰量子多体物理。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on new states of electronic matter in materials. Materials derive their properties from their microscopic building blocks; atoms and molecules, and, in particular, the electrons that we often envision as swirling around atomic nuclei. In metals a fraction of the electrons disassociate from individual atoms and migrate through the system, while in other materials all electrons remain localized. In either case, the electrons give materials the electrical and magnetic properties that are exploited in electronics components and other technological applications. This project aims at increasing our understanding of the ways in which electrons can form a wealth of different complex states due to their interactions with each other. The interactions depend on the specific material which hosts the electrons. Being microscopic particles, the motion and interactions of electrons are governed by quantum mechanics, and it is technically challenging to construct tractable theoretical models to describe them, and to understand and tailor their properties. In this project, models of interacting electrons are studied under conditions relevant to, for example, high temperature superconductor materials formed by copper-oxide layers separated from each other by other atoms. In these materials electrons form a new state of matter, superconductivity, which can conduct electricity without loss or resistance at temperatures where oxygen would be a liquid. The models are studied using large-scale computer simulations. At the heart of the project is to understand how an insulating magnet is transformed into new magnetic states when a model parameter, for example describing electron interaction, is changed, and how additional electrons injected into this state behave. Understanding this model system may be key to understanding the physical origins of superconductivity in these materials and may provide a key to the discovery of new materials which exhibit superconductivity at higher temperatures opening avenues to technological applications such as low loss power transmission and new kinds of electronic devices. In addition to its scientific significance, the project aims to train graduate students in state-of-the-art physical modeling and computer simulations, and to help develop user-friendly software for other researchers applying the methods and models developed.TECHNICAL SUMMARYThis award supports theoretical research and education on new states of electronic matter in materials. An important aspect of condensed matter physics is to study ground states and excitations of strongly correlated quantum-matter systems for example, localized spins of highly frustrated quantum magnets or valence electrons of cuprate high temperature superconductors. Quantum field-theory descriptions often contain emergent ingredients, such as spinons, holons, and gauge fields, which are proposed on the basis of phenomenology and symmetry arguments. The field theories are typically only solvable in certain limits. This research focuses on utilizing numerically exact quantum Monte Carlo techniques to study microscopic Hamiltonians, which can be tuned to various regimes where emergent particles and fields can be detected by studying low-energy physics. These studies can be related to field-theory results, and also can yield experimentally detectable signatures of unconventional collective electronic states. This research can therefore bridge lattice-scale physics and emergent low-energy behavior, with potential impact on theoretical as well as experimental research on correlated quantum matter. The PI will study J-Q models in which the magnetically ordered ground state of a 2D quantum antiferromagnet can be destroyed, leading to a quantum phase transition to a non-magnetic state with emergent local singlets that form a valence-bond solid. These models appear to host unconventional low-energy quantum objects which can be interpreted as spinons and a U(1) gauge field. The PI will address how these particles and fields emerge from the lattice scale up to large length-scales accessible with powerful simulation techniques tailored to the models. The main objectives are: (i) To relate the excitations of J-Q models to gauge field theory, in particular to explore analogies of the Higgs mechanism and Higgs boson in systems close to the quantum phase transition between the antiferromagnet and the valence-bond solid. (ii) To introduce mobile charge carriers which presumably would lead to holons, and explore connections with the "strange metal" state of the cuprate high temperature superconductors. New and improved simulation algorithms will be developed as an integral part of the project and these have broad applications in condensed matter physics as well as in research on ultra-cold atomic condensates and systems of interest in the quantum information research. The models and methods are also of interest in high-energy particle physics, providing a simpler setting than standard lattice gauge-field theory to study non-perturbative quantum many-body physics.