Quantum Critical Phenomena and Non Fermi Liquid Physics

量子临界现象与非费米液体物理

• 批准号: 1308236
• 负责人: Andrew Millis
• 金额: $ 33万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-05-15 至 2017-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1308236&HistoricalAwards=false
• 关键词: Quantum; Critical; Phenomena; Non; Fermi

NONTECHNICAL SUMMARYThis award supports theoretical and computational research to advance understanding of strongly interacting electrons in equilibrium and in situations far from the steady state of equilibrium. Superconductivity, magnetism, conversion of light into electrical energy: the astonishing variety of behavior found in `electrically active' materials arise from the combination of quantum mechanics and the electrical repulsion between electrons. Understanding this behavior is one of the grand challenges of modern science. Controlling it would create new technologies that can improve all of our lives. However this `many electron' problem is one of the classic hard problems of theoretical science. The research supported by this award builds on exciting recent developments in computers, algorithms and physics concepts, some of them invented by the PI, that are transforming the capability to solve these problems. The PI will further develop, implement and use these new ideas and new computational methods to understand, design, optimize and exploit materials with new kinds of important electronic properties. A central focus of this research is to use the new methods to understand what happens when an electrically active material is challenged by an applied current, electrical impulse, or light wave, because how a material responds to such a challenged determines its technological utility. TECHNICAL SUMMARYThis award supports theoretical and computational studies of the physics of strongly interacting electrons in both equilibrium and nonequilibrium situations. A key aspect of the proposed research is the further development and wider application of new classes of computational methods that the PI and other groups have recently introduced. New methods are needed because the combination of quantum mechanical entanglement and electron-electron interactions makes the many-electron problem formally unsolvable for large systems. The difficulties are compounded in the nonequilibrium situation, which is relevant to devices and to new classes of pump-probe experiments, where even the basic theoretical concepts are unclear. The PI will build on discoveries made by many NSF-supported researchers over the years, relating to the use of stochastic methods, such as Monte Carlo, to estimate the value of a Feynman diagram series. These methods have opened up wide classes of previously intractable problems to quantitative investigation. The PI will use them to gain new insights into the superconducting properties of novel materials by constructing and studying in detail the superconducting and pseudogap states of the two dimensional Hubbard model and relating these to the magnetic properties which can now be calculated using the vertex correction methodology developed in the previous funding period. The PI will also explore new applications of the stochastic exploration of diagram series approach to the nonequilibrium case. The straightforward extensions the PI pioneered in previous funding periods do not permit access to physics on long-time scales, but new work based on expansions around analytically determined partial resummations seems to allow access to the long-time limit. The PI will use these methods to develop solvers for the equations of nonequilibrium dynamical mean field theory. In a third research thrust the PI will use analytical methods to examine the interplay of superconducting, antiferromagnetic and `nematic' phases and fluctuations in the iron-pnictide superconductors.

非技术性总结该奖项支持理论和计算研究，以促进对平衡态和远离平衡稳态的情况下强相互作用电子的理解。超导性、磁性、将光转化为电能：在“电活性”材料中发现的令人惊讶的各种行为是由量子力学和电子之间的电排斥力的结合引起的。理解这种行为是现代科学的重大挑战之一。控制它将创造新的技术，可以改善我们所有人的生活。然而，这个“多电子”问题是理论科学的经典难题之一。该奖项支持的研究建立在计算机，算法和物理概念的令人兴奋的最新发展基础上，其中一些由PI发明，正在改变解决这些问题的能力。PI将进一步开发，实施和使用这些新的想法和新的计算方法来理解，设计，优化和开发具有新的重要电子特性的材料。 这项研究的一个中心焦点是使用新方法来了解当电活性材料受到施加的电流，电脉冲或光波的挑战时会发生什么，因为材料如何响应这种挑战决定了它的技术效用。该奖项支持在平衡和非平衡情况下强相互作用电子物理学的理论和计算研究。拟议的研究的一个关键方面是PI和其他团体最近推出的新类别的计算方法的进一步发展和更广泛的应用。 需要新的方法，因为量子力学纠缠和电子-电子相互作用的结合使得多电子问题在大型系统中形式上无法解决。在非平衡态情况下，困难更加复杂，这与设备和新的泵探测实验有关，甚至基本的理论概念都不清楚。 PI将建立在多年来许多NSF支持的研究人员所做的发现的基础上，这些发现涉及使用随机方法，如蒙特卡洛，来估计费曼图系列的值。这些方法已经开辟了广泛的类以前难以解决的问题进行定量研究。PI将使用它们来获得新的见解，通过构建和详细研究二维哈伯德模型的超导和赝能隙状态，并将其与现在可以使用在上一个资助期开发的顶点校正方法计算的磁性相关联，来了解新材料的超导特性。PI还将探索图表系列随机探索方法在非平衡情况下的新应用。PI在以前的资助期间开创的直接扩展不允许在长时间尺度上访问物理学，但基于围绕分析确定的部分重复的扩展的新工作似乎允许访问长时间限制。PI将使用这些方法来开发非平衡动力学平均场理论方程的求解器。在第三个研究重点中，PI将使用分析方法来研究铁磷族化合物超导体中超导、反铁磁和“铁”相的相互作用以及波动。