Applications of Field Theory to Condensed Matter Physics

这笔拨款为凝聚态理论的研究提供了支持。其目的是了解包含强耦合自由度的凝聚态系统，特别是拓扑相和电子液晶相的相图和量子临界行为。拓扑相是物质的状态，它没有序参量，因此不是自发对称性破缺的产物，而是具有一种“量子序”，其中基态简并程度由它们所在空间的拓扑决定。电子液晶相是强关联电子以不均匀和各向异性的方式自组织的物质状态，与高温超导机制密切相关。将研究的相关课题包括量子霍尔系统和强耦合结中的量子相干和干涉现象，以及电子液晶相与高温超导的关系。这些问题的性质需要量子场论的方法和思想。这是解决涉及强相互作用系统的统计和量子物理问题的最佳工具。它使这项研究能够利用凝聚态物质系统和高能物理之间持续和相互丰富的思想交流。智力上的优点：这项研究解决了一系列重要和困难的问题，这些问题是目前非常活跃的基础物理领域的肥沃领域。更广泛的影响：这笔赠款使有才华的研究人员的继续培训成为可能。这位首席研究员在培训学生和博士后方面有着出色的记录，他与西班牙裔和女性科学家的工作尤其值得注意。%这项拨款支持现代凝聚态物理学的核心研究。特别是，首席研究员将应用先进的理论技术来研究相互作用强烈的电子的奇异相。除了对这些相和相关现象(如高温超导)的基本兴趣外，这些研究还可能导致新材料和器件的发现。这项研究为学生提供了良好的训练基础。

This grant provides support for research into the theory of condensed matter. The objective is to understand condensed matter systems involving strongly coupled degrees of freedom, and in particular the phase diagram and quantum critical behavior of topological phases and electronic liquid crystal phases. Topological phases are states of matter that do not have an order parameter, and are therefore not the product of spontaneous symmetry breaking, but posses a kind of "quantum order" in which the ground state degeneracy is determined by the topology of the space in which they live. Electronic liquid crystal phases are states of matter in which strongly correlated electronic organize themselves in inhomogeneous and anisotropic patterns, and are closely related with mechanisms of high temperature superconductivity. Related topics that will be investigated include quantum coherence and interference phenomena in quantum Hall systems and strongly coupled junctions, and the relation between electronic liquid crystal phases and high temperature superconductivity.The nature of the problems to be studied requires the methods and ideas of quantum field theory. This is the best tool with which to attack problems involving the statistical and quantum physics of strongly interacting systems. It enables this research to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems and high energy physics.Intellectual Merit: The research addresses a range of important and difficult problems in currently fertile, and therefore very active, areas of fundamental physics. Broader Impact: The grant makes possible the continued training of talented researchers. The principal investigator has an excellent record training students and postdoctoral associates, and his work with Hispanic and female scientists is particularly noted.%%%This grant supports research that is at the core of modern condensed matter physics. In particular, the principal investigator will apply advanced theoretical techniques to the study of exotic phases of electrons that interact strongly with each other. Besides the fundamental interest in these phases and associated phenomena, e.g., high temperature superconductivity, these studies may lead to the discovery of new materials and devices. The research provides an excellent training ground for students.