Quantum cluster methods for strongly correlated materials

长期以来，我们对材料的理解一直基于简单的范式：金属可以用偶尔发生碰撞的准独立电子来理解；在另一个极端，磁体可以用定域电子的自旋来理解。但在这些范例之间存在着一系列材料，即使它们可能显示出两者的特征，但就这些简单的图片而言，它们是无法理解的。近30年前发现的高温超导体就是这种“强关联材料”的原型。这类材料表现出各种迷人的性质，从超导到奇特的磁性、电荷顺序等。它们具有巨大的潜力。基于这些性质的技术进步将受到对强相关材料的更深入理解的指导。*这项提议的目标有两个：(1)开发计算工具来理解和计算强相关材料的性质；(2)将这些方法应用于各种系统，其中一些是通用的，另一些是代表真实材料的。

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, discovered nearly 30 years ago, are the prototype of such "strongly correlated materials". Such materials display a variety of fascinating properties, from superconductivity to exotic magnetism, charge order, etc. They have tremendous potential. Technological advances based on these properties will be guided by a deeper understanding of strongly correlated materials.***The objective of this proposal is two-fold: (1) to develop computational tools to understand and calculate properties of strongly correlated materials and (2) to apply these methods to a variety of systems, some generic, other representing real materials.