Quantum Fluctuations and Broken Symmetries in Correlated Electron Systems

该奖项支持对各种问题的理论研究和教育，当电子相关性很重要时，这些问题由量子涨落和破缺对称性的共同线索相互联系。这个项目将解决：铜酸盐中的高温超导性，耗散量子相变，特别是在低维系统中，如纳米线，以及适用于许多凝聚态物质系统的量子相变中的无序作用，从铜酸盐到重费米子再到有机物。最近在铜超导体中量子振荡的发现开启了这个20年来未解决的物理学重大问题的新时代。对这一现象的理论认识可能会带来重大突破。PI的方法是对各种破对称状态进行建模，特别注意在涡旋液态中竞争阶参数的共存状态。PI将采用精确传递矩阵技术和朗道尔-皮查德公式来计算舒布尼科夫-德哈斯振荡。耗散量子相变的讨论是因为它们在揭示量子力学基础方面的潜在重要性，以及它们在新型量子临界性中的关键作用，具有许多应用。数值模拟和标度理论将被使用。该理论的一个具体应用是正在进行的纳米线量子相滑移实验。在同样广泛的框架下，PI还将研究相变，特别是量子相变中的无序作用。许多对理解相关电子系统非常重要的复杂材料不可避免地充满了无序。这两种工具的严格数学统计力学以及数值模拟在定义良好的量子模型将被解决。在许多情况下，可能需要一些非正统的思维；量子力学纠缠熵的概念，冯·诺伊曼熵，就是其中之一。该奖项还支持培养理论凝聚态物理方面的研究生。研究活动将加强本科生的教学，因为现在有更多的少数民族和女学生。正是在这个本科阶段，PI将鼓励学生追求科学事业。该奖项支持量子相变的理论研究和教育。这是一个深入研究的现象，已成为凝聚态物理的前沿研究。普通的相变，如水到冰的转变，发生在非零温度下，并由热波动驱动。由海森堡测不准原理的量子涨落驱动，量子相变可以在温度的绝对零度发生。该项目旨在探索近年来在这种新视角下发现的新材料，并解释它们可观察到的、迄今为止令人困惑的特性。这项研究可能会在预测有用材料方面取得进一步的进展，比如在室温下可能表现出超导性的材料。超导是物质的一种量子力学状态，到目前为止，这种状态发生在低温下，最多大约是大气中气态成分氮元素沸腾的低温的两倍。超导体可以不损耗地传输电力。与此同时，我们将学习物质量子特性的基本方面。这项研究可能会导致对可能构成未来技术基础的新材料的进一步理解。该奖项还支持培养理论凝聚态物理方面的研究生。研究活动将加强本科生的教学，因为现在有更多的少数民族和女学生。正是在这个本科阶段，PI将鼓励学生追求科学事业。

TECHNICAL SUMMARYThis award supports theoretical research and education on a variety of problems that are interlinked by the common threads of quantum fluctuations and broken symmetries when electronic correlations are important. This project will address: high temperature superconductivity in cuprates, dissipative quantum phase transitions in general, and in particular, in low dimensional systems such as nanowires, and the role of disorder in quantum phase transitions applicable to many condensed matter systems, from cuprates to heavy fermions to organics. The recent discovery of quantum oscillations in cuprate superconductors has ushered in a new era of this twenty-year old unsolved major problem in physics. A theoretical understanding of this phenomenon may result in a major breakthrough. The PI's approach is to model the various broken symmetry states, with particular attention paid to coexisting states of competing order parameters in the vortex liquid state. The PI will employ exact transfer matrix technique and Landauer-Pichard formula to compute Shubnikov-de Haas oscillations. Dissipative quantum phase transitions are addressed because of their potential importance in shedding light on the foundations of quantum mechanics, as well as their key role in a novel class of quantum criticality, with many applications. Numerical simulations as well as scaling theories will be used. A specific application of the theory is the ongoing experiments in quantum phase slips in nanowires. In the same broad framework, the PI will also investigate the role of disorder in phase transitions, in particular quantum phase transitions. Many complex materials of great importance in understanding correlated electron systems are inevitably rife with disorder. Both the tools of rigorous mathematical statistical mechanics as well as numerical simulations in well-defined quantum models will be addressed. There are many cases where some unorthodox thinking may be required; the notion of quantum mechanical entanglement entropy, the von Neumann entropy, is one of them. This award also supports training graduate students in theoretical condensed matter physics. Research activities will enhance teaching in undergraduate classes, where there are now many more minorities and women students. It is at this undergraduate level that the PI will encourage students to pursue careers in science.NONTECHNICAL SUMMARYThis award supports theoretical research and education on quantum phase transitions. These are an intensely studied phenomenon that has become cutting edge research in condensed matter physics. Ordinary phase transitions, like the transition of water to ice, take place at non-zero temperature and are driven by thermal fluctuations. Quantum phase transitions can take place at the absolute zero of temperature driven by the quantum fluctuations of Heisenberg's uncertainty principle. The PI aims to explore novel materials that have been discovered in recent years in this new light and to explain their observable, and so far puzzling, properties. This research may lead to further progress in predicting useful materials, such as materials that might exhibit superconductivity at room temperatures. Superconductivity is a quantum mechanical state of matter that so far occurs at low temperatures, at most about twice the frigid temperature where the element nitrogen, a gaseous component of our atmosphere, boils. Superconductors can carry electricity without loss. At the same time we would be learning fundamental aspects of quantum properties of matter. This research may lead to further understanding of novel materials that may form the foundations of future technologies.This award also supports training graduate students in theoretical condensed matter physics. Research activities will enhance teaching in undergraduate classes, where there are now many more minorities and women students. It is at this undergraduate level that the PI will encourage students to pursue careers in science.