Applications of Field Theory to Condensed Matter Physics

技术综述：该奖项支持对新物质状态的理论研究。我们的目标是理解包含许多强耦合自由度的凝聚态系统，这些系统的行为受量子力学的强烈影响。这种强关联体系中的电子自发地组织成电子液晶相和拓扑相。这是一个前沿研究领域，在这个领域中，对物理学中一些最基本问题的理解是通过在技术前沿进行的实验来实现的。电子液晶相是强相关电子以不均匀和各向异性图案组织起来的物质状态。它们与高温超导的机制密切相关，高温超导是物理学中的一个基本问题，已经在技术上产生了强烈的影响。拓扑相是物质的量子流体状态，它没有序参量，因此不破坏任何对称性，但具有一种隐藏的量子秩序，其中基态简并程度由它们所在空间的拓扑决定。拓扑流体的量子态是强纠缠的，这一性质可以用来设计拓扑量子计算机，这是物理和数学中的一个前沿问题，对技术具有巨大的潜在影响。将研究的相关课题包括电子液晶与高温超导的关系，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研究的问题的本质需要使用量子场论的方法和思想。这些是解决涉及强相互作用系统的统计和量子物理问题的最好工具。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思想交流。非技术概述：该奖项支持旨在预测新的物质状态并发展对其新性质的基本理解的理论研究。这项研究的重点将是从相互强烈相互作用的电子中出现的物质状态，并将其限制在两个维度上。这项研究的一个重点是物质的激发态，理论上预测，在垂直于电子片的强磁场中，这种物质存在于电子片中。这些条件可以在特殊的半导体结构中实现。物质的状态，称为拓扑态，还有待实验证实。这项研究的一个挑战是提出能够明确检测到它们并了解它们的性质的实验。了解这些物质的状态是如何被控制的，可能会导致一种新型的计算机，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，并且能够比目前的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的量子力学状态。处于这些状态的电子以某种方式自我组织，这样它们就可以像液体一样流动，但呈现出取向和对称的图案，这让人想起原子在固体中的排列方式。最近的实验支持了这些态的存在，这些态被认为对理解高温超导体起到了重要作用。这项研究涉及到材料物理的前沿问题，并为培养下一代理论科学家提供了极好的机会。它还为未来的技术打开了新的可能性。

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.