Disordered Systems, Supersymmetry, and Topological Phases

无序系统、超对称性和拓扑相

• 批准号: 0706195
• 负责人: Nicholas Read
• 金额: $ 41.75万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0706195&HistoricalAwards=false
• 关键词: Disordered; Systems; Supersymmetry; Topological; Phases

TECHNICAL SUMMARY:This award supports theoretical research and education in low temperature phenomena in both classical and quantum condensed matter systems. Specifically, these include the quantum Hall regime in a two-dimensional electron gas in a high magnetic field, with the goal of understanding the non-Abelian topological phases of matter in this and other systems. Included in the investigations is the possibility of using such systems for topological quantum computation. Another focus is disordered systems, including non-interacting fermions in two dimensions as in the integer quantum Hall effect, with the use of algebraic techniques applied to lattice models and conformal field theory of critical points. Disordered systems arising from optimization and their connections with statistical physics problems such as spin glasses will also be addressed.NON-TECHNICAL SUMMARY:This award supports theoretical research and education in theoretical condensed matter physics at the interface with mathematics. With the discovery that the electric conductivity of thin materials sandwiched into thin layers in a magnetic field was fixed to certain discrete amounts, that was the beginning of research on the quantum hall effect. The electrons confined to a thin layer exhibit unusual structures because of the quantum mechanical laws that govern motion for small particles at small distances. This has proven to be an extraordinarily rich topics because of the many usual behaviors, some reflecting new states of matter. Research in this grant involves the specific topics of electrons confined to layers and includes some investigation of new states of matter associated with the fractional quantum hall effect. Since the prediction of these new states of matter, it has also become possible that the unusual properties of some of them could be the basis for new kinds of computers, so called topological quantum computers. The operation of these computers would be particularly resistant to noise from the environment that normally spoils essential properties of quantum mechanical states. Learning more about these exotic quantum systems so that they may be of potential technological value requires highly sophisticated mathematics and the creativity behind theoretical physics. The ideas and fundamental knowledge generated by endeavors such as these contribute to future technologies not yet envisioned, but contribute to the foundation of this Nation's future success in global economic competition.

技术概述：该奖项支持在经典和量子凝聚态系统低温现象的理论研究和教育。具体来说，这些包括高磁场下二维电子气体中的量子霍尔制度，目的是了解该系统和其他系统中物质的非阿贝尔拓扑相。在研究中包括使用这种系统进行拓扑量子计算的可能性。另一个重点是无序系统，包括二维的非相互作用费米子，如整数量子霍尔效应，使用代数技术应用于晶格模型和临界点的共形场理论。由优化引起的无序系统及其与统计物理问题（如自旋玻璃）的联系也将被讨论。非技术总结：该奖项支持理论凝聚态物理与数学界面的理论研究和教育。由于发现夹在磁场中薄层的薄材料的电导率固定在一定的离散量，这是量子霍尔效应研究的开始。由于控制小粒子在小距离上运动的量子力学定律，被限制在薄层上的电子表现出不同寻常的结构。这已经被证明是一个非常丰富的话题，因为许多通常的行为，一些反映了物质的新状态。这项拨款的研究涉及限于层内电子的特定主题，并包括与分数量子霍尔效应相关的物质新状态的一些研究。由于预测了这些物质的新状态，其中一些不寻常的特性也有可能成为新型计算机的基础，即所谓的拓扑量子计算机。这些计算机的运行将特别能抵抗来自环境的噪声，这些噪声通常会破坏量子力学状态的基本属性。更多地了解这些奇异的量子系统，以便它们可能具有潜在的技术价值，需要高度复杂的数学和理论物理背后的创造力。这些努力所产生的思想和基础知识对未来的技术做出了不可想象的贡献，但也为美国未来在全球经济竞争中取得成功奠定了基础。