Quantum Fluctuations and Broken Symmetries in Correlated Electron Systems

该奖项支持理论研究和教育的各种问题，这些问题是由量子波动和打破对称性的共同线索时，电子相关性是重要的。该项目将涉及：铜酸盐中的高温超导性、一般而言的耗散量子相变，特别是在诸如纳米线的低维系统中的耗散量子相变，以及无序在适用于从铜酸盐到重费米子到有机物的许多凝聚态系统的量子相变中的作用。最近在铜氧化物超导体中发现的量子振荡，为这个20年未解决的物理学重大问题开辟了一个新时代。对这一现象的理论理解可能会带来重大突破。PI的方法是对各种对称性破缺状态进行建模，特别注意涡旋液态中竞争序参数的共存状态。PI将采用精确的传递矩阵技术和Landauer-Pichard公式计算Shubnikov-de哈斯振荡。耗散量子相变是解决，因为它们在揭示量子力学的基础上的潜在重要性，以及它们在一类新的量子临界性中的关键作用，具有许多应用。数值模拟以及缩放理论将被使用。该理论的一个具体应用是正在进行的纳米线量子相位滑移实验。在同一个广泛的框架内，PI还将研究无序在相变中的作用，特别是量子相变。许多复杂的材料在理解相关电子系统中具有重要意义，但它们不可避免地充满了无序。严格的数学统计力学工具以及在定义良好的量子模型中的数值模拟都将得到解决。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，冯诺依曼熵，就是其中之一。该奖项还支持理论凝聚态物理学研究生的培训。研究活动将加强本科班的教学，现在本科班的少数民族学生和女学生要多得多。正是在这个本科阶段，PI将鼓励学生追求科学事业。非技术性总结这个奖项支持量子相变的理论研究和教育。这是一个被深入研究的现象，已经成为凝聚态物理学的前沿研究。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。量子相变可以发生在绝对零度的温度下，由海森堡测不准原理的量子涨落驱动。PI的目的是探索近年来在这种新的光线下发现的新材料，并解释它们可观察到的，迄今为止令人困惑的性质。这项研究可能会导致预测有用材料的进一步进展，例如可能在室温下表现出超导性的材料。超导性是一种量子力学状态的物质，到目前为止，它发生在低温下，最多大约是我们大气中气态成分氮元素沸腾的寒冷温度的两倍。超导体可以无损耗地输送电力。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。该奖项还支持理论凝聚态物理学的研究生培训。研究活动将加强本科班的教学，现在本科班的少数民族学生和女学生要多得多。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.