New Paradigms of Quantum Criticality

该奖项支持旨在描述现代量子材料的物理性质与多粒子量子纠缠性质之间联系的理论研究。金属和半导体中电子运动的传统理论通常是在由其他电子定义的平均环境中独立地处理每个电子的运动。这种独立的电子图像在许多金属和半导体中已经相当成功。然而，在许多新发现的材料中，一些具有重要技术意义的材料，需要解释电子之间微妙的量子相关性，甚至需要理解它们的宏观性质。特别是，导致“幽灵般的远距离作用”的量子纠缠不仅可以出现在一对电子之间，也可以出现在长距离和涉及大量电子的情况下。在这项研究中特别感兴趣的一类材料是铜高温超导体，所有这些材料都是层状材料，包含排列在方形晶格中的铜和氧原子层。越来越多的实验证据表明，在移动电子密度附近存在一个“量子临界点”，在那里可以观察到超导性的最高临界温度。本理论研究将描述电子纠缠在这一临界点上的相变。PI和其他人已经开发了描述许多粒子纠缠的新方法，并且跨越了物理学的不同领域，包括量子信息理论，高能粒子理论和量子引力。这些进展将在新的理论框架中综合，并通过对量子材料的观察进行测试。该奖项还将通过支持在理论凝聚态物理前沿课题的研究生和博士后的培训，为科学劳动力的发展做出贡献。此外，公团将继续积极开展公开讲座、采访、座谈会、高等研究生学校讲座等活动。技术概述：该奖项支持理论研究，将研究涉及规范理论与有限密度物质耦合的量子临界模型。虽然我们对规范理论与2+1时空维度的相对论性物质耦合的相变有很多了解，但铜临界性的应用需要有限密度的费米子物质，在没有无序的情况下，它有一个尖锐的费米表面。PI和他的研究小组提出了铜临界的特定规范理论，该理论满足了观测所施加的许多现象学约束。在某些数学背景下，规范结构和费米表面的结合导致有效的量子场论在时间上是双局部的。目前，人们对这种2+1维的双局部理论知之甚少，解开这一谜团将是本研究的一个重要重点。以前，双局部理论已经出现在具有无限范围相互作用的模型中，如Sachdev-Ye-Kitaev （SYK）模型，它具有一些吸引人的现象学特征。从SYK模型的研究中获得的见解将应用于本研究中出现的更现实的双域场理论。研究的另一个重点领域将是热霍尔效应：在最近的实验中，热霍尔效应已经成为与纠缠结构变化相关的量子相变的强大诊断探针。PI和他的团队将把热霍尔效应的理论扩展到铜合金的赝隙相模型中。此外，将研究扭曲石墨烯双层中的相关电子超导性，重点关注多竞争序和超导性的量子相互作用。该奖项还将通过支持在理论凝聚态物理前沿课题的研究生和博士后的培训，为科学劳动力的发展做出贡献。此外，公团将继续积极开展公开讲座、采访、座谈会、高等研究生学校讲座等活动。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 award supports theoretical research aimed at describing the connection between physical properties of modern quantum materials and the nature of many-particle quantum entanglement. Conventional theories of electron motion in metals and semiconductors usually treat the motion of each electron independently, in an average environment defined by the other electrons. This independent electron picture has been quite successful in many metals and semiconductors. However, in many newly discovered materials, some of significant technological importance, the subtle quantum correlations between the electrons need to be accounted for, even for an understanding of their macroscopic properties. In particular, quantum entanglement leading to “spooky action at a distance” can be present not only between a pair of electrons, but across long distances and involving large numbers of electrons. A class of materials of particular interest in this research are the cuprate high temperature superconductors, all of which are layered materials containing layers with copper and oxygen atoms arranged in a square lattice. There is accumulating experimental evidence for a "quantum critical point" near a mobile electron density where the highest critical temperature for superconductivity is observed. This theoretical research will describe the phase transition in the electron entanglement across this critical point. New methods for describing many particle entanglement have been developed by the PI and others, and also across different fields of physics, including quantum information theory, high energy particle theory, and quantum gravity. These advances will be synthesized in new theoretical frameworks, and subjected to tests by observations on quantum materials. This award will also contribute to the development of the scientific workforce by supporting the training of graduate students and postdoctoral associates in topics at the forefront of theoretical condensed matter physics. Furthermore, the PI will continue to pursue an active program of public lectures, interviews, colloquia, and lectures at schools for advanced graduate students. TECHNICAL SUMMARYThis award supports theoretical research which will examine models of quantum criticality involving gauge theories coupled to finite density matter. While much is known about phase transitions of gauge theories coupled to relativistic matter in 2+1 spacetime dimensions, applications to cuprate criticality require finite density fermionic matter which, in the absence of disorder, has a sharp Fermi surface. The PI and his research team have proposed specific gauge theories for cuprate criticality which satisfy numerous phenomenological constraints imposed by observations. In some mathematical contexts, the combination of the gauge structure and the presence of a Fermi surface leads to effective quantum field theories which are bilocal in time. Currently, little is understood about such bilocal theories in 2+1 dimensions, and unraveling this mystery will be an important focus of this research. Previously, bilocal theories have appeared in models with infinite-range interactions, like the Sachdev-Ye-Kitaev (SYK) models, which have some attractive phenomenological features. Insights gained from the study of SYK models will be applied to the more realistic bilocal field theories appearing in this research. Another focus area of the research will be on the thermal Hall effect: In the most recent experiments, the thermal Hall effect has emerged as a powerful diagnostic probe of quantum phase transitions associated with changes in entanglement structure. The PI and his team will extend theories of the thermal Hall effect to models of the pseudogap phase of the cuprates. In addition, correlated electron superconductivity in twisted graphene bilayers will be studied, with a focus on the quantum interplay of multiple competing orders and superconductivity.This award will also contribute to the development of the scientific workforce by supporting the training of graduate students and postdoctoral associates in topics at the forefront of theoretical condensed matter physics. Furthermore, the PI will continue to pursue an active program of public lectures, interviews, colloquia, and lectures at schools for advanced graduate students.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.