Strongly correlated quantum materials

今天的工业很大程度上依赖于先进材料，这些材料从发现到商业产品的发展需要几十年的时间。即使是美国的私人基金会，如摩尔基金会和西蒙斯基金会，也承认并支持基础研究，这些研究将提供丰富的实用信息，企业家和创新者将能够利用这些信息开发新产品和新工艺。这类基础研究对加拿大、对美国和世界同样重要。参与基础知识发展的学生将特别有能力认识到这些知识带来的机会，并了解应用基础研究所需工具的优点和局限性。我们将通过专注于“强相关量子材料”来为这一努力做出贡献，即具有明显量子行为和集体效应的材料，这些材料从基本角度来看是有趣的，同时在技术上也是相关的。这个为期五年的研究计划有两大类目标。第一个方向使用目前可用的最强大的方法，其中一些是我的小组开发的，来预测强相互作用量子材料的性质。具体的例子包括强相关超导性。超导体无电阻输电，在宏观尺度上表现出量子效应。室温下的超导性将给技术带来革命性的变化。强相关超导性将理论方法推向了最困难的领域，即在金属-绝缘体跃迁附近，在那里电子的局域化和波动图像同样重要。超导性在这种金属-绝缘体过渡附近是最强的，无论是通过添加/去除导电电子引起的，如在基于铜-氧平面（铜酸盐）的陶瓷中，还是由压力引起的，如在层状有机化合物中。通过保持这种总体观点，将铜酸盐和层状有机物放在同一框架内考虑，我们可以牢固地确定哪些方法可以为我们提供强相关超导性的预测理论。第二个方向是开发新的方法，利用量子模拟器（如冷原子）作为基准，并利用其他领域（如量子信息）的见解来预测和提出新量的测量。事实上，尽管使用量子力学最基本概念的传统理论方法足以获得构成当前电子技术的材料的基本知识，但它们不足以用于强相关量子材料。我们正在解决现代物理学的一个重大挑战：开发必要的工具来处理材料的微妙量子力学方面，以做出有用的预测。

Much of today's industry relies on advanced materials whose development from discovery to commercial product takes decades. Even private foundations in the United States, such as the Moore foundation and the Simons foundation, recognize and support fundamental research that will provide a wealth of practical information that entrepreneurs and innovators will be able to use to develop new products and processes. This type of fundamental research is as important for Canada as it is for the United States and the world. The students that will participate in the development of fundamental knowledge will be especially skilled to recognize the opportunities brought about by this knowledge and to understand the advantages and limitations of the tools necessary to apply fundamental research. We will contribute to this effort by focusing on "Strongly Correlated Quantum Materials", namely materials with pronounced quantum behavior and collective effects that lead to a host of properties that are intriguing from a fundamental point of view, while also technologically relevant. This five-year research program has two broad classes of objectives. The first direction uses the most powerful methods currently available, some of which my group has developed, to predict properties of strongly interacting quantum materials. Specific examples include strongly-correlated superconductivity. Superconductors transport electricity without resistance and manifest quantum effects at macroscopic scales. Superconductivity at room temperature would revolutionize technology. Strongly-correlated superconductivity pushes theoretical methods in the most difficult regime, namely in the vicinity of a metal-insulator transition, where the localized and wave picture of electrons are equally important. Superconductivity is strongest near this metal-insulator transition, whether it is induced by adding/removing conduction electrons, as in ceramics based on copper-oxygen planes (cuprates), or by pressure, as in layered organic compounds. By keeping this general point of view, where cuprates and layered organics are considered within the same framework, we can firmly establish which methods give us a predictive theory of strongly correlated superconductivity. The second direction develops new methods, taking advantage of quantum simulators such as cold atoms for benchmarks, and taking advantage of insights from other fields, such as quantum information, to predict and propose measurements of new quantities. Indeed, although traditional theoretical methods using the most elementary notions of quantum mechanics were sufficient to obtain the basic knowledge that gave us the materials that make up current electronic technology, they are inadequate for strongly correlated quantum materials. We are addressing a grand challenge of modern physics: developing the tools necessary to handle subtle quantum mechanical aspects of materials to make useful predictions.