Numerical simulation of the physical spin and charge response of correlated materials

相关材料的物理自旋和电荷响应的数值模拟

• 批准号: RGPIN-2017-04253
• 负责人: Leblanc, James
• 金额: $ 1.53万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=678491
• 关键词: Numerical; simulation; physical; spin; charge

Electrons are the objects that form current in metals, semi-conductors and insulators. Modern day electronic devices are possible due to our ability to understand and control how electrons move in materials, or react when exposed to light or an applied voltage. Surprisingly, our understanding of precisely how electrons behave in materials is very rudimentary. The root cause of this problem is that the complex interactions between electrons scale exponentially with the number of electrons, which is on the order of Avogadro's constant (6.02x1023). This means that we cannot overcome this many electron problem by simply building bigger or faster computers, but instead require innovative and novel approaches to estimate solutions with less computational expenditure. *** My research program over the next five years will be centered around the development of new numerical procedures to tackle this many-body problem for strongly correlated electron systems; systems that exhibit both metallic and insulating behaviour. (I) We will use statistical methods, known as Quantum Monte Carlo which avoid exponential scaling with system complexity. These methods will be applied to model systems, in order to test and improve our numerical algorithms. To begin, we will study the Hubbard model, which is the quintessential model of correlated electron systems. Over the course of this program, we will extend beyond the restrictions of that model to allow more general non-local interactions. This will allow us to take incremental steps from purely theoretical model systems, towards real material calculations. ***(II) As a secondary component of the program, as we develop well tested software codes for handling correlated electron systems, these will be used to solve problems on the short term. This work will be focused on understanding the roles of spin and charge degrees of freedom in the cuprate superconductors, a long standing and open problem in the field of high temperature superconductivity.*** The detailed understanding of interacting systems, and the interplay between spin and charge degrees of freedom will allow for the intelligent design of materials and will therefore be of impact to both fundamental research programs and promote technological development in industry.

电子是在金属、半导体和绝缘体中形成电流的物体。 现代电子设备之所以成为可能，是因为我们有能力理解和控制电子如何在材料中移动，或者在暴露于光或施加电压时发生反应。 令人惊讶的是，我们对电子在材料中的行为的精确理解是非常基本的。 这个问题的根本原因是电子之间的复杂相互作用与电子数量呈指数关系，其数量级为阿伏伽德罗常数（6.02x1023）。 这意味着我们不能通过简单地建造更大或更快的计算机来克服这么多电子的问题，而是需要创新和新颖的方法来估计具有更少计算开销的解决方案。 * 我的研究计划在未来五年将围绕新的数值程序的发展，以解决这个多体问题的强相关电子系统;系统表现出金属和绝缘行为。 (I)我们将使用称为量子蒙特卡罗的统计方法，它避免了系统复杂性的指数扩展。 这些方法将被应用到模型系统，以测试和改进我们的数值算法。 开始，我们将研究Hubbard模型，这是关联电子系统的典型模型。 在这个程序的过程中，我们将超越该模型的限制，以允许更一般的非局部相互作用。 这将使我们能够从纯理论的模型系统逐步走向真实的材料计算。* （II）作为该计划的第二部分，当我们开发出处理相关电子系统的经过良好测试的软件代码时，这些代码将用于解决短期问题。 这项工作将侧重于理解铜酸盐超导体中自旋和电荷自由度的作用，这是高温超导领域长期存在的开放问题。 对相互作用系统的详细了解，以及自旋和电荷自由度之间的相互作用将允许材料的智能设计，因此将对基础研究计划和促进工业技术发展产生影响。