Topological Phases, Supersymmetry, and Disordered Systems

技术总结材料研究部和数学科学部为该奖项提供资金。它支持经典和量子凝聚态系统中低温现象领域的理论研究和教育。具体地说，这些包括在强磁场中出现在二维电子气中的电子气的量子霍尔区，目的是更深入地了解这个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。另一个焦点是无序系统，包括二维的非相互作用费米子，如整数量子霍尔效应，使用应用于晶格模型和临界点的共形场论的代数技术。优化产生的无序系统及其与统计物理问题的联系，如经典自旋玻璃，也将被讨论。虽然研究将集中于加深对基本性质的理解，但将尽可能将其应用于实验。非技术总结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交界处的理论研究和教育。夹在半导体之间的电子在强磁场中形成薄层的导电能力是以离散的数量固定的。理论预测，这些显着的量子霍尔效应表明，磁场中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州的性质的研究。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同寻常的性质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抵抗来自环境的噪音，这些噪音通常会破坏量子力学状态的基本性质。学习更多关于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。这样的努力产生的想法和基础知识有助于未来的技术，但有助于这个国家未来在全球经济竞争中取得成功的基础。

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.