CAREER: Quantum Entanglement and Geometric Frustration in Correlated Metals

非技术性总结这个职业支持在金属系统的量子凝聚态物理学的长期存在的概念问题的研究和教育。随着温度的降低，大多数材料都以一种或另一种方式排列。例如，水分子在低温下形成冰晶。然而，存在一种有趣的可能性，即材料即使在绝对零度下也不有序;这种材料被称为“量子液体”。过去十年的重大理论发现之一是，量子液体具有一个独特的量子性质：它们是高度纠缠的物体。在纠缠量子系统中，单个组件的状态不能独立于其他组件来描述。在量子液体中，大约有一万亿万亿个粒子可以相互纠缠！由于其反直觉的性质，量子纠缠可能提供令人兴奋的应用，从超快计算到新颖的加密方案。然而，与此同时，纠缠往往是脆弱的。因此，一个关键问题是：在哪里寻找具有强大纠缠的材料？PI和他的团队将开发一种多管齐下的方法，通过结合理论物理，量子信息科学和最先进的计算算法的工具来研究高度纠缠的材料。发展适当的理解将使研究人员能够做出精确的预测，这对于利用量子纠缠的技术潜力至关重要。另一个理想的目标是利用计算机科学的思想对强相互作用的物质进行更深入的理解。这些进展可能会同时影响多个科学研究领域，从量子材料到高能粒子物理和量子信息科学。所开发的算法和软件会以公开源码的形式向社会发放。为配合研究计划，首席研究员会举办和参与多项教育和外展活动。首先，PI将尝试通过介绍PI的研究来给本科生带来量子物理学的兴奋。第二，PI将每年举办一次讲习班，对象是社会经济处境不利的高中生，讲习班将培养他们制定与日常生活相关的估计数的技能。最后，PI将指导本科生和研究生的研究课题密切配合的研究组件。技术总结这个职业生涯支持在金属系统的量子凝聚态物理学的长期存在的概念问题的研究和教育。具体来说，PI将集中在材料的问题，无论是不符合朗道的费米液体理论，或其描述仅在传统的破坏秩序参数错过关键的物理方面。连接这些材料的一个共同点是它们是高度量子纠缠的。为了取得进展，PI将在量子信息理论，量子场论和最先进的量子蒙特卡罗（QMC）技术的交叉点上开发新的想法和工具。理解强关联金属的最大障碍之一是费米子符号问题。当费米子进一步耦合到几何上受抑的自旋时，问题就复杂了。这样的设置是直接相关的各种各样的挫折重费米子系统。为了在这方面取得进展，PI将实施一种新发现的算法，该算法首次允许对一大类受挫的Kondo晶格系统进行无偏模拟。这种方法也将揭示挫折金属系统的纠缠结构。PI还将从量子信息论的角度研究重费米子的全局相图。这项研究的预期成果是：1）对一大类哈密顿量的预测能力，这些哈密顿量模拟了与量子技术潜在相关的相关金属。2)关联金属整体相图的量子信息论理解。3)开发新的计算算法，能够解决与量子物理学不同领域相关的广泛问题，从凝聚态物理学到原子物理学和高能粒子物理学。所开发的算法和软件会以公开源码的形式向社会发放。为配合研究计划，首席研究员会举办和参与多项教育和外展活动。首先，PI将尝试通过介绍PI的研究来给本科生带来量子物理学的兴奋。第二，PI将每年举办一次讲习班，对象是社会经济处境不利的高中生，讲习班将培养使用与日常生活相关的数量级估计的技能。最后，PI将指导本科生和研究生的研究课题密切配合的研究组成部分。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

NONTECHNICAL SUMMARYThis CAREER supports research and education on long-standing conceptual questions in the quantum condensed matter physics of metallic systems. Most materials order in one pattern or another as the temperature decreases. For example, water molecules order to form ice crystals at low temperatures. However, there exists an interesting possibility whereby a material doesn't order even at the absolute zero temperature; such materials go by the moniker "quantum liquids". One of the major theoretical discoveries of the past decade is that quantum liquids are distinguished by a feature of exclusively quantum nature: they are highly entangled objects. In an entangled quantum system, the state of an individual component cannot be described independently of the other components. In a quantum liquid, approximately a trillion trillion particles can be entangled with each other! Due to its counter-intuitive properties, quantum entanglement potentially offers exciting applications ranging from ultrafast computing to novel encryption schemes. At the same time, however, entanglement can often be fragile. Therefore, a key question is: where to look for materials with robust entanglement?The PI and his group will develop a multipronged approach to study highly entangled materials by combining tools from theoretical physics, quantum information science, and state-of-the-art computational algorithms. Developing proper understanding will allow the researchers to make precise predictions, which is essential for harnessing the technological potential of quantum entanglement. Another desired goal is to develop a deeper understanding of strongly interacting matter using ideas from computer science. Such progress will potentially impact several areas of scientific inquiry at once, ranging from quantum materials to high-energy particle physics and quantum information science. The algorithms and software developed will be disseminated to the community in open-source form.In tandem with the research project, the PI will organize and participate in a variety of educational and outreach activities. Firstly, the PI will try to bring the excitement of quantum physics to undergraduates by presenting introductory lectures on the PI's research. Secondly, the PI will organize a yearly workshop aimed at socio-economically disadvantaged high-school students, which will develop skills in formulating estimates relevant for everyday life. Finally, the PI will mentor undergraduate and graduate students on research topics closely aligned with the research component.TECHNICAL SUMMARYThis CAREER supports research and education on long-standing conceptual questions in the quantum condensed matter physics of metallic systems. Specifically, the PI will focus on questions informed by materials which either do not fit within Landau's Fermi liquid theory, or whose description solely in terms of conventional symmetry-breaking order parameters misses key physical aspects. A common thread connecting these materials is that they are highly quantum entangled. To make progress, the PI will develop new ideas and tools at the intersection of quantum information theory, quantum field theory and state-of-the-art Quantum Monte Carlo (QMC) techniques. One of the big impediments in understanding strongly correlated metals is the Fermion sign problem. The problem is compounded when the fermions are further coupled to geometrically frustrated spins. Such a set-up is directly relevant for a wide variety of frustrated heavy-fermion systems. To make progress on this front, the PI will implement a newly discovered algorithm that for the first time allows for unbiased simulations of a large class of frustrated Kondo lattice systems. This approach will also shed light on the entanglement structure of frustrated metallic systems. The PI will also study the global phase diagram of heavy fermions from a quantum-information-theoretic perspective.The expected outcomes of this research are: 1) Predictive power on a large class of Hamiltonians that model correlated metals potentially relevant for quantum technologies. 2) A quantum-information-theoretic understanding of the global phase diagram of correlated metals. 3) Development of new computational algorithms that will be capable of addressing a wide range of problems relevant to distinct areas of quantum physics, from condensed matter physics to atomic physics and high-energy particle physics. The algorithms and software developed will be disseminated to the community in open-source form.In tandem with the research project, the PI will organize and participate in a variety of educational and outreach activities. Firstly, the PI will try to bring the excitement of quantum physics to undergraduates by presenting introductory lectures on the PI's research. Secondly, the PI will organize a yearly workshop aimed at socio-economically disadvantaged high-school students, which will develop the skill of using order-of-magnitude estimates relevant for everyday life. Finally, the PI will mentor undergraduate and graduate students on research topics closely aligned with the research component.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.