Phases of Correlated Quantum Matter

该奖项支持强相关电子材料和量子临界性的理论研究和教育。量子物质的相可以具有独特的违反直觉的性质，例如可以流动而没有粘性的超流体，以及表现出导电而没有耗散的超导体。量子力学在高温超导体等材料中起着至关重要的作用。PI计划研究这些材料中可能存在的各种量子相。量子临界性是这项研究的另一个焦点;它的影响可以在实验可测量的温度下感受到。通过这些研究，PI旨在帮助了解许多这些材料所表现出的不寻常特性，其中一些具有潜在的技术应用。该研究还将有助于为研究其他更多样化的复杂系统开发可靠的理论工具。这些都是基于这样的观察，即物质的相在相域上延伸，其中通常大部分域仅包含少量的耦合自由度。因此，要理解物质的相，不必像在临界点那样处理具有无限相关长度的系统（技术上是一项非常困难的任务），但处理具有短相关长度的系统就足够了，并且有强大的方法可用于此目的。这种局部区域或小簇的确切性质可以使用计算机来发现，然后可以使用分析工具来理解这些局部区域如何在固体中耦合。同样，通过明智地选择有效的哈密顿量，可以使相关的阶段更容易分析。这项工作的更广泛的影响包括训练研究生在学术和工业环境中担任领导角色，不仅通过在家乡机构指导学生，还通过鼓励他们参加专业会议，在那里他们可以展示他们的研究活动的成果，并与该领域的其他人交换意见。在过去的赠款期间，一名女研究生获得了博士学位。并将努力招募更多的少数民族。正在计划将研究活动纳入凝聚态物理学的现代研究生教科书，并利用网络有效地推广研究生教育。非技术总结：该奖项支持理论研究和教育，重点是理解与电子相互作用强烈的材料类别相关的不寻常性质和现象。这些材料包括高温超导体。这项研究的一个特殊焦点是一种称为量子临界性的现象，它与物质如何集体组织成不同阶段的基本问题有关。一块冰和一杯水是完全不同的，尽管基本的组成部分，水分子，是相同的。当水被冷却到273.15 K或0.C以下时，发生转变，水变成冰。一个更壮观的现象，已成为凝聚态物理学的前沿研究，是可以在绝对零度下发生的相变。在这种情况下，一个物理变量，如磁场强度、原子分离或无序度，所起的作用类似于水变成冰的例子中温度的作用。量子力学的一个基本原理提供了跃迁的驱动力。PI将开发理论技术，以更好地理解量子相变以及它们如何导致令人兴奋的新现象，如高温超导性或复杂材料的不寻常特性。这些都为未来的器件和材料技术奠定了基础。这项工作的更广泛的影响涉及培训研究生承担学术和工业环境中的领导角色，不仅通过指导学生在家庭机构，而且还通过鼓励他们参加专业会议，在那里他们可以展示他们的研究活动的结果，并与该领域的其他人交换意见。在过去的赠款期间，一名女研究生获得了博士学位。并将努力招募更多的少数民族。正在计划将研究活动纳入凝聚态物理学的现代研究生教科书，并利用网络有效地推广研究生教育。

TECHNICAL SUMMARY:This award supports theoretical research and education on strongly correlated electron materials and quantum criticality. Phases of quantum matter can have unique counterintuitive properties, such as superfluids which can flow without viscosity, and superconductors which exhibit electric conduction without dissipation. Quantum mechanics plays an essential role in such materials as high-temperature superconductors and many others that continue to be discovered.The PI plans to study a variety of quantum phases that can exist in such materials. Quantum criticality is another focus of this resesarch; its effects can be felt at experimentally measurable temperatures. Through these studies the PI aims to contribute to understanding the unusual properties exhibited by many of these materials, some having potential technological applications. The research will also help to develop reliable theoretical tools for the study of other more diverse complex systems. These are based on the observation that a phase of matter extends over a phase domain where typically much of the domain contains only a small number of coupled degrees of freedom. Therefore, to understand phases of matter, it is not necessary to treat systems with infinite correlation length (technically a very difficult task), as at a critical point, but it is sufficient to treat systems with short correlation lengths, and there are powerful methods available for this purpose. The exact properties of such local regions or small clusters can be fond using computers, and then analytical tools can be used to understand how these local regions are coupled in a solid. Similarly, by judiciously choosing the effective Hamiltonian, one can make a relevant phase more accessible to analysis.The broader impacts of this work involve training graduate students to assume leadership roles in academic and industrial environments, not only by mentoring students at the home institution, but also by encouraging them to attend professional meetings, where they can present results of their research activities and exchange ideas with others in the field. During the past grant period one woman graduate student got her Ph.D. and an effort will be made to recruit more minorities. Plans are underway to incorporate research activities into a modern graduate textbook in condensed matter physics and to use the web for effective outreach for graduate level education. NON-TECHNICAL SUMMARY:This award supports theoretical research and education that focuses on understanding the unusual properties and phenomena associated with classes of materials in which electrons interact strongly with each other. These materials include the high temperature superconductors. A partcular focus of this research is a phenomenon called quantum criticality which is related to the fundamental problem of how matter collectively organizes itself into distinct phases. A block of ice is as distinct as it can be from a cup of water, although the fundamental constituents, the water molecules, are identical. When water is cooled below the temperature 273.15 K or 0.C, a transformation occurs where water turns into ice. An even more spectacular phenomenon which has become cutting edge research in condensed matter physics is a transformation among phases that can take place at the absolute zero of temperature. In this case, a physical variable, like magnetic field strength, atomic separation, or degree of disorder, plays a role analogous to that of temperature in the example of water to ice. A fundamental principle of quantum mechanics provides the driving force of the transition. The PI will develop theoretical techniques to better understand quantum phase transformations and how they might lead to exciting new phenomena, like high temperature superconductivity, or unusual properties of complex materials. These contribute to the foundations of future device and materials technologies. The broader impacts of this work involve training graduate students to assume leadership roles in academic and industrial environments, not only by mentoring students at the home institution, but also by encouraging them to attend professional meetings, where they can present results of their research activities and exchange ideas with others in the field. During the past grant period one woman graduate student got her Ph.D. and an effort will be made to recruit more minorities. Plans are underway to incorporate research activities into a modern graduate textbook in condensed matter physics and to use the web for effective outreach for graduate level education.