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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=710951
• 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，是因为我们能够理解和控制电子在材料中的运动方式，或者当暴露在光或外加电压下时发生反应的能力。令人惊讶的是，我们对电子在材料中的确切行为的理解是非常初级的。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，约为阿伏加德罗常数(6.02x1023)的数量级。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许多电子问题，相反，我们需要创新和新颖的方法来估计解决方案，而不是更少的计算支出。 我未来五年的研究计划将集中在开发新的数值程序，以解决强关联电子系统的这个多体问题；强关联电子系统既表现出金属行为，又表现出绝缘行为。(I)我们将使用被称为量子蒙特卡罗的统计方法，这种方法避免了系统复杂性的指数缩放。这些方法将应用于模型系统，以测试和改进我们的数值算法。首先，我们将研究Hubbard模型，这是关联电子系统的典型模型。在本计划的过程中，我们将超越该模型的限制，允许更一般的非本地交互。这将使我们能够逐步从纯粹的理论模型系统转向真正的材料计算。 (2)作为该计划的一个次要组成部分，随着我们为处理相关电子系统开发经过充分测试的软件代码，这些代码将被用来在短期内解决问题。这项工作将集中于了解自旋和电荷自由度在铜酸盐超导体中的作用，这是高温超导领域一个长期存在的悬而未决的问题。 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，将使材料的智能设计成为可能，因此将对基础研究计划和促进工业技术发展产生影响。