Topological Phases, Supersymmetry, and Disordered Systems

技术摘要材料研究部和数学科学部为该奖项提供资金。它支持在经典和量子凝聚态系统低温现象领域的理论研究和教育。具体来说，这些包括发生在高磁场中的二维电子气体中的电子气体的量子霍尔制度，其目标是更深入地理解该系统和其他系统中物质的非阿贝尔拓扑相。现在有大量的实验和理论工作旨在将这种系统用于拓扑量子计算。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（如经典自旋玻璃）的联系也将被讨论。虽然研究将集中于加深对基本特性的理解，但将尽可能将其应用于实验。材料研究部和数学科学部为该奖项提供资金。它支持凝聚态物理和数学界面的理论研究和教育。在高磁场中，夹在半导体薄层之间的电子导电的能力是固定的，数量是离散的。理论预测，这些显著的量子霍尔效应表明，磁场中的二维电子可以将自己组织成微妙的新物质状态。该奖项支持进一步探索这些状态本质的研究。自从他们的预测以来，人们已经意识到，这些新物质状态的不寻常特性可以构成新型计算机的基础，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。更多地了解奇异的量子力学系统和材料，并揭示它们的技术价值，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。

TECHNICAL SUMMARYThe Division of Materials Research and the Division of Mathematical Sciences provide funds for this award. It supports theoretical research and education in the area of low-temperature phenomena in both classical and quantum condensed matter systems. Specifically, these include the quantum Hall regime of an electron gas that occurs 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 in greater depth. There is now a large experimental and theoretical effort aimed at 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 classical spin glasses will also be addressed. While the research will concentrate on deepening the understanding of fundamental properties, applications to experiments will be made wherever possible.NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Mathematical Sciences provide funds for this award. It supports theoretical research and education at the interface of condensed matter physics and mathematics. The ability of electrons sandwiched between semiconductors into thin layers in a high magnetic field to conduct electricity is fixed in discrete amounts. Theory predicts that these remarkable quantum Hall effects signal that electrons in two dimensions in a magnetic field can organize themselves into subtle new states of matter. This award supports research that further explores the nature of these states. Since their prediction, it has been realized that the unusual properties of these new states of matter can form 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 exotic quantum mechanical systems and materials and revealing their 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.