Applications of Field Theory to Condensed Matter Physics

该奖项支持对新物质状态的理论研究。目的是了解凝聚态系统，包括许多强耦合的自由度，其行为是由量子力学的强效应。这种强关联系统中的电子自发地组织在电子液晶相和拓扑相中。这是一个前沿的研究领域，其中物理学中一些最基本的问题的理解是通过在技术的前沿进行实验来实现的。电子液晶相是物质的状态，其中强关联的电子以不均匀和各向异性的模式组织自己。它们与高温超导机制密切相关，这是物理学中的一个基本问题，已经对技术产生了强烈的影响。拓扑相是物质的量子流体态，它们没有序参量，因此不会破坏任何对称性，但具有一种隐藏的量子序，其中基态简并由它们所处空间的拓扑决定。拓扑流体的量子态是强纠缠的，这一性质可用于设计拓扑量子计算机，这是物理学和数学中的前沿问题，对技术具有巨大的潜在影响。研究的相关课题包括电子液晶相与高温超导性的关系、量子霍尔系统中的量子相干和干涉现象、量子纠缠和拓扑量子计算。PI研究的问题的本质要求使用量子场论的方法和思想。这些是解决强相互作用系统的统计和量子物理问题的最佳工具。这种方法使该项目能够利用凝聚态系统，高能物理和数学之间持续和相互丰富的交叉施肥思想。非技术摘要：该奖项支持旨在预测新物质状态并对其新颖性质进行基本理解的理论研究。研究的重点将是从电子中出现的物质状态，这些电子相互作用强烈，并且局限于二维空间。研究的一个重点是物质的激发态，理论上预测这些物质存在于垂直于电子片的强磁场中。这些条件可以在特殊的半导体结构中实现。物质的状态，称为拓扑状态，还有待实验证实。研究的一个挑战是提出可以明确检测它们并了解它们的特性的实验。了解这些物质状态如何被控制可能会导致一种新型计算机，这种计算机依赖于有目的地操纵量子力学状态来进行操作，并且能够比现有计算机更快地进行某些计算。研究的另一个重点是进一步理解PI和合作者提出的电子的新量子力学状态。处于这些状态的电子以某种方式组织自己，使它们可以像液体一样流动，但表现出的取向和对称性模式让人想起原子在固体中的排列方式。最近的实验支持这些状态的存在，这些状态被认为在理解高温超导体中起着重要作用。这项研究涉及材料物理学中的前沿问题，并为培养下一代理论科学家提供了极好的机会。它还为未来技术开辟了新的可能性。

TECHNICAL SUMMARY:This award supports theoretical research on new states of matter. The objective is to understand condensed-matter systems involving many strongly coupled degrees of freedom whose behavior is governed by strong effects of quantum mechanics. The electrons in such strongly correlated systems organize spontaneously in electronic liquid crystal phases and topological phases. This is a frontier area of research in which the understanding of some of the most fundamental problems in physics is achieved by experiments done at the cutting edge of technology. Electronic liquid crystal phases are states of matter in which strongly correlated electrons organize themselves in inhomogeneous and anisotropic patterns. They are closely related to mechanisms of high temperature superconductivity, a fundamental problem in physics which already has had a strong impact in technology. Topological phases are quantum fluid states of matter that do not have an order parameter, and therefore do not break any symmetry, but possess a kind of hidden quantum order in which the ground state degeneracy is determined by the topology of the space in which they live. The quantum states of a topological fluid are strongly entangled, a property that can be used to devise a topological quantum computer, a frontier problem in physics and mathematics having great potential impact on technology. Related topics that will be investigated include the relation between electronic liquid crystal phases and high temperature superconductivity, quantum coherence and interference phenomena in quantum Hall systems, quantum entanglement and topological quantum computing.The nature of the problems the PI studies requires the use of the methods and ideas of quantum field theory. These are the best tools with which to attack problems involving the statistical and quantum physics of strongly interacting systems. Such an approach enables the project to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems, high energy physics, and mathematics.NON-TECHNICAL SUMMARY:This award supports theoretical research that aims to predict new states of matter and to develop fundamental understanding of their novel properties. The emphasis of the research will be on states of matter that emerge from electrons that interact strongly with each other and are confined to two dimensions. One focus of the research is on exciting states of matter that are theoretically predicted to exist in a sheet of electrons in a strong magnetic field perpendicular to the sheet. These conditions can be realized in special semiconductor structures. The states of matter, called topological states, have yet to be confirmed experimentally. A challenge of the research is to propose experiments that can unambiguously detect them and to understand their properties. Understanding how these states of matter can be controlled may lead to a new kind of computer that depends on the purposeful manipulation of quantum mechanical states for its operation and would be able to carry out certain calculations much more rapidly than current computers. Another focus of the research is to further understand new quantum mechanical states of electrons that have been proposed by the PI and collaborators. The electrons in these states organize themselves in a way so that they can flow like a liquid but exhibit patterns of orientation and symmetry that are reminiscent of the way atoms are arranged in a solid. Recent experiments support the existence these states which are proposed to play an important role in understanding the high temperature superconductors.The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientist. It also opens new possibilities for future technologies.