CAREER: Quantum Entanglement and Geometric Frustration in Correlated Metals

本职业支持金属系统量子凝聚态物理中长期存在的概念性问题的研究和教育。随着温度的降低，大多数材料以一种或另一种模式排列。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”。在过去的十年里，一个重要的理论发现是量子液体有一个独特的量子特性：它们是高度纠缠的物体。在纠缠量子系统中，单个组分的状态不能独立于其他组分来描述。在量子液体中，大约有一万亿亿个粒子可以相互纠缠！由于其反直觉的特性，量子纠缠可能提供令人兴奋的应用，从超高速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，通过结合理论物理学、量子信息科学和最先进的计算算法来研究高度纠缠的材料。发展正确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。另一个期望的目标是利用计算机科学的思想对强相互作用物质有更深的理解。这样的进展可能会同时影响几个科学研究领域，从量子材料到高能粒子物理和量子信息科学。开发的算法和软件将以开源的形式向社区传播。为了配合研究计划，PI将组织和参与各种教育和外展活动。首先，PI将尝试通过介绍PI研究的入门讲座，将量子物理的兴奋带给本科生。第二，PI将每年组织一次针对社会经济上处于不利地位的高中生的讲习班，这些讲习班将培养制定与日常生活有关的估算的技能。最后，PI将指导本科生和研究生的研究课题与研究组成部分密切相关。本职业支持金属系统量子凝聚态物理中长期存在的概念性问题的研究和教育。具体来说，PI将关注那些不符合朗道费米液体理论的材料，或者仅仅根据传统的对称破缺顺序参数描述而忽略了关键物理方面的问题。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将在量子信息论、量子场论和最先进的量子蒙特卡罗（QMC）技术的交叉领域开发新的想法和工具。理解强相关金属的一大障碍是费米子符号问题。当费米子与几何上受挫的自旋进一步耦合时，问题就变得复杂了。这种设置与各种各样受挫的重费米子系统直接相关。为了在这方面取得进展，PI将实现一种新发现的算法，该算法首次允许对大量受挫的近藤晶格系统进行无偏模拟。这种方法也将揭示受挫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。这项研究的预期结果是：1)对一大类哈密顿量的预测能力，这些哈密顿量可以模拟与量子技术潜在相关的相关金属。2)相关金属整体相图的量子信息理论理解。3)开发新的计算算法，能够解决与量子物理不同领域相关的广泛问题，从凝聚态物理到原子物理和高能粒子物理。开发的算法和软件将以开源的形式向社区传播。为了配合研究计划，PI将组织和参与各种教育和外展活动。首先，PI将尝试通过介绍PI研究的入门讲座，将量子物理的兴奋带给本科生。其次，PI将每年组织一次针对社会经济上处于不利地位的高中生的讲习班，该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与研究组成部分密切相关。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.