Quantum Effects in Low-Dimensional Systems

技术总结该奖项支持凝聚态物理的理论研究和教育。两个中心研究课题是(I)强烈起伏的量子磁性，通常是在低维，以及(Ii)石墨烯和石墨中的输运和界面物理。磁学工作的主要目标是使用几种方法来表征量子无序相的物理特性。一种这样的方法是通过使用量子纠缠光谱，它已经被证明可以产生关于分数量子霍尔效应态的边缘激发的详细信息。这一分析线利用了分数量子霍尔效应和自旋链之间的一些深层次联系。在角动量空间中分割分数量子霍尔效应波函数等价于相应的自旋链波函数在动量空间中的倒易分割，揭示了某些无间隙系统的体激发谱信息。这项研究的另一个方向是推广价键固态并研究它们的性质，例如S=1阿弗莱克、肯尼迪、利布和塔萨基链中的“隐藏”弦序，它是霍尔丹相的象征。我们将研究对SU(N)自旋和单重态的推广，以及相应的高维分数量子霍尔效应波函数。关于石墨烯的工作将集中在石墨烯和石墨中的结和界面，包括单层和双层石墨烯之间的结，以及与石墨烷的结。我们将研究周期势在有外场和无外场的情况下的影响。在石墨中，涡轮层状材料的c轴输运将与晶体位错的电子结构一起建模。这项工作的教育内容包括研究生的培训和为研究生和高级本科生编写详细的、书本质量的课堂讲稿。非技术总结该奖项支持凝聚态物理的理论研究和教育。研究工作将集中在两个主要主题上：(I)微观层面的磁性，和(Ii)石墨烯，这是一个单原子厚度的碳原子平面片。一条共同的线索是，许多研究的系统本质上是一维或二维的。低维量子磁学为凝聚物界提供了一些引人注目的、令人信服的“量子无序”相的范例--物质的状态，在这种状态下，量子力学波动，即使在尽可能低的温度下，也会导致经典秩序的“融化”。争论的焦点是如何描述这些无序的相。最近的一种方法使用纠缠，这是一个本质上的量子力学概念，来描述这种状态。一维量子磁体和二维电子气在强磁场中的深层联系也将被开发和研究。石墨烯具有一种不同寻常的电子结构，在这种结构中，携带电荷的激发表现得好像它们是无质量的，这让人想起光子，即光的量子。这里的研究工作将集中在石墨烯中的大规模不均匀，包括单层和多层石墨烯之间的界面，以及石墨堆积模式的破坏。在这两种情况下，都将调查电子传导的后果。这是为未来设备技术的智力基础做出贡献的基础研究。特别是，石墨烯具有独特的性质，使其成为包括未来电子设备在内的各种应用的有前途的材料。这项提议的教育方面包括培养物理学博士生，以及进一步为高级本科生和物理学研究生开发广泛的详细、书本质量的课堂讲稿。

TECHNICAL SUMMARYThis award supports theoretical research and education in condensed matter physics. The two central research topics are (i) strongly fluctuating quantum magnetism, typically in low dimensions, and (ii) transport and interfacial physics in graphene and graphite. The major objective in the magnetism work is to characterize the physics of quantum-disordered phases using several approaches. One such approach is through the use of quantum entanglement spectra, which have been shown to yield detailed information regarding the edge excitations of fractional quantum Hall effect states. This line of analysis exploits some deep connections between the fractional quantum Hall effect and spin chains. Partitioning the fractional quantum Hall effect wavefunctions in angular momentum space is equivalent to a reciprocal momentum space partitioning of the corresponding spin chain wavefunctions, and reveals information about the bulk excitation spectra in certain gapless systems. Another direction of this research is in the generalization of valence bond solid states and an investigation of their properties, such as the "hidden" string order in the S=1 Affleck, Kennedy, Lieb, and Tasaki chain, which is emblematic of the Haldane phase. Generalizations to SU(N) spins and to singlets extended over N-site simplices will be investigated, along with corresponding higher-dimensional fractional quantum Hall effect wavefunctions.The work on graphene will focus on junctions and interfaces in graphene and graphite, including junctions between monolayer and bilayer graphene, and also with graphane. The effects of periodic potentials will be studied, both with and without external fields. In graphite, the c-axis transport of the turbostratic material will be modeled, along with the electronic structure of crystalline dislocations.The educational elements of this work include the training of a graduate student and the development of detailed, book-quality, lecture notes for graduate students and advanced undergraduates.NONTECHNICAL SUMMARYThis award supports theoretical research and education in condensed matter physics. The research effort will focus on two main topics: (i) magnetism at the microscopic level, and (ii) graphene, which is a one-atom-thick planar sheet of carbon atoms. A common thread is that many of the systems studied are intrinsically one-dimensional or two-dimensional.Low-dimensional quantum magnetism has provided the condensed matter community with some remarkable and compelling paradigms of "quantum-disordered" phases - states of matter where quantum mechanical fluctuations, even at the lowest possible temperatures, lead to a "melting" of classical order. At issue is how to characterize these disordered phases. A recent approach uses entanglement, an intrinsically quantum-mechanical concept, to characterize such states. Deep connections between one-dimensional quantum magnets and two-dimensional electron gases in a strong magnetic field will also be exploited and investigated.Graphene has an unusual electronic structure, in which charge carrying excitations behave as if they are massless, reminiscent of photons, the quanta of light. The research effort here will focus on large-scale inhomogeneities in graphene, including interfaces between single and multilayer graphene, and disruptions in the stacking pattern of graphite. In both cases, the consequences for electronic conduction will be investigated.This is fundamental research that contributes to the intellectual foundations of future device technologies. Graphene, in particular, has unique properties that make it a promising material for various applications including future electronic devices.The educational aspects of this proposal include the training of a PhD student in physics, and the further development of an extensive collection of detailed, book-quality lecture notes for advanced undergraduates and physics graduate students.