Quantum cluster methods and their applications to quantum materials

量子簇方法及其在量子材料中的应用

• 批准号: RGPIN-2020-05060
• 负责人: Sénéchal, David
• 金额: $ 2.99万
• 依托单位: Université de Sherbrooke
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740376
• 关键词: Quantum; cluster; methods; their; applications

Our understanding of materials has long been based on simple paradigms: metals can be understood in terms of quasi-independent electrons, undergoing occasional collisions; at the other extreme, magnets are understood in terms of the spins of localized electrons. But between these paradigms lies a spectrum of materials that defy comprehension in terms of these simple pictures, even though they may show characteristics of both. High-temperature superconductors are the prototype of such "strongly correlated quantum materials". Such materials can display a variety of fascinating properties, from superconductivity to exotic magnetism, charge ordering, transitions between insulating and conducting behavior, spontaneous violation of the time-reversal symmetry, etc. Technological advances based on these properties will be guided by a deeper understanding of strongly correlated quantum materials at a fundamental level. The objective of this proposal is two-fold: (1) to develop computational tools to understand and calculate properties of strongly correlated quantum materials and (2) to apply these methods to a variety of systems, some generic, other representing real materials. Even the simplest theoretical models that we can devise to describe these materials cannot be solved with the traditional theorist's pen and paper. They require the use of supercomputers and of sophisticated approximation strategies. Part of our effort is to make our understanding of quantum materials more quantitative, by using models that are closer to real materials, or by applying our methods with a higher degree of accuracy. Another part of our effort is to make the relevant computational tools easier to use and widely available. Physical systems that we propose to study include high-temperature superconductors, superconducting strontium ruthenate, twisted bilayer graphene, heterostructures made of high-temperature superconductors and topological insulators. Computational tools that we propose to improve on include cluster dynamical mean field theory and tensor network methods. This is a program of fundamental, not applied research. Much of today's economy rests on fundamental discoveries made many decades ago (e.g. semiconductors). Private foundations (e.g. the Moore foundation and the Simons foundation in the US) understand the importance of investing in fundamental research on new materials, even though decades may be necessary before applications of these materials are commonplace. Students trained within this research program will develop skills that will be useful in a wide range of research activities, both fundamental and applied: critical thinking, computational skills, data analysis, etc.

长期以来，我们对材料的理解都基于简单的范式：金属可以用准独立的电子来理解，偶尔会发生碰撞；在另一个极端，磁体是根据局域电子的自旋来理解的。但在这些范式之间存在着一系列材料，这些材料无法通过这些简单的图片来理解，尽管它们可能显示出两者的特征。高温超导体就是这种“强关联量子材料”的原型。此类材料可以表现出各种令人着迷的特性，从超导性到奇异磁性、电荷排序、绝缘和导电行为之间的转变、时间反转对称性的自发破坏等。基于这些特性的技术进步将由更深入的理解来指导在基本水平上强相关量子材料的研究。该提案的目标有两个：（1）开发计算工具来理解和计算强相关量子材料的特性；（2）将这些方法应用于各种系统，一些是通用的，另一些代表真实材料。即使我们能够设计出描述这些材料的最简单的理论模型，也无法用传统理论家的笔和纸来解决。它们需要使用超级计算机和复杂的近似策略。我们努力的一部分是通过使用更接近真实材料的模型，或者通过应用更高精度的方法，使我们对量子材料的理解更加定量。我们努力的另一部分是使相关计算工具更易于使用和广泛使用。我们拟研究的物理系统包括高温超导体、超导钌酸锶、扭曲双层石墨烯、高温超导体异质结构和拓扑绝缘体。我们建议改进的计算工具包括簇动态平均场理论和张量网络方法。 这是一个基础研究项目，而不是应用研究项目。当今的经济很大程度上依赖于几十年前的基本发现（例如半导体）。私人基金会（例如美国的摩尔基金会和西蒙斯基金会）了解投资新材料基础研究的重要性，尽管这些材料的应用可能需要几十年的时间才能普及。在该研究项目中接受培训的学生将培养在基础和应用等广泛研究活动中有用的技能：批判性思维、计算技能、数据分析等。