Theoretical studies of quantum magnets and strongly correlated metals

量子磁体和强相关金属的理论研究

• 批准号: RGPIN-2020-05615
• 负责人: Curnoe, Stephanie
• 金额: $ 1.75万
• 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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=763211
• 关键词: Theoretical; studies; quantum; magnets; strongly

The goal of this research program is to discover and study theoretical frameworks which capture the general underlying and unifying physical principles of quantum materials such as frustrated magnets and strongly correlated metals. Geometrically frustrated magnets are characterized by the geometry of their magnetic ion sub-lattice: the magnetic moments ("spins") are located at the vertices of triangles or tetrahedra. Generally, a pair of spins has a particular relative orientation which minimizes their interaction energy. A system is frustrated when there is no arrangement of the spins that simultaneously minimizes the interaction energy between all pairs of spins. A famous example is the rare-earth pyrochlore crystals, where the magnetic rare earth ions are located on the vertices of a connected network of tetrahedra. Many different phenomena have been observed in pyrochlore crystals, including ordinary ferromagnetism (a state where the spins are all aligned with each other), anti-ferromagnetism (in which the spins alternate their orientation), spin ice (systems with spins obeying the ice-rule: two spins pointing into and two spins pointing out of each tetrahedron), quantum spin-ice (spin-ice states with large quantum fluctuations) and spin-liquid (a state that has macroscropic quantum entanglement). The proposed research will develop and use a suite of computational and analytical methods. The foundation for all approaches is the model, and in crystals with a high underlying symmetry, completely general models will be derived using the methods of group theory (symmetry); these same methods can greatly reduce the complexity of the models. Computational methods include exact diagonalization (which yields exact solutions for systems with a small number of spins) and classical spin simulations. Strongly correlated metals are conductors in which there are strong interactions between electrons, yielding a rich phase diagram that includes metal-to-insulator transitions, superconductivity or magnetic order. The electronic correlations can be modeled by the Hubbard interaction: a strong, constant repulsion that inhibits more than one conduction electron from occupying each atomic site. Although conceptually simple, this model presents difficult computational challenges, even in two-dimenstions. Recent advances by our group at MUN, which combine analytic and computational methods in a procedure called "Algorithmic Matsubara Integration" have considerably decreased computing times to the point where exact results up to sixth order in perturbation theory are within reach. This proposal aims to fulfill this task. Beyond two-dimensions, the Hubbard model has been applied to many systems, especially those with transition elements or rare earths. Among these are the metallic rare-earth pyrochlores such as Pr2Ir2O7; the longer term goal of this work is to apply our numerical techniques to this system.

该研究计划的目标是发现和研究理论框架，捕捉量子材料（例如受挫磁体和强相关金属）的一般基础和统一物理原理。几何挫败磁体的特征在于其磁离子子晶格的几何形状：磁矩（“自旋”）位于三角形或四面体的顶点。一般来说，一对自旋具有特定的相对方向，这使得它们的相互作用能最小化。当自旋排列不能同时最小化所有自旋对之间的相互作用能时，系统就会受挫。一个著名的例子是稀土烧绿石晶体，其中磁性稀土离子位于四面体相连网络的顶点上。在烧绿石晶体中观察到许多不同的现象，包括普通铁磁性（自旋彼此对齐的状态）、反铁磁性（自旋交替方向）、自旋冰（自旋服从冰-铁磁性的系统）规则：两个自旋指向每个四面体，两个自旋指向每个四面体），量子自旋冰（具有大量子涨落的自旋冰态）和自旋液体（具有大量子涨落的状态）宏观量子纠缠）。 拟议的研究将开发和使用一套计算和分析方法。所有方法的基础是模型，在具有高度基础对称性的晶体中，将使用群论（对称性）的方法导出完全通用的模型；这些相同的方法可以大大降低模型的复杂性。计算方法包括精确对角化（为具有少量自旋的系统产生精确解）和经典自旋模拟。强关联金属是电子之间存在强相互作用的导体，产生丰富的相图，包括金属到绝缘体的转变、超导性或磁序。电子相关性可以通过哈伯德相互作用来建模：一种强烈的、恒定的排斥力，抑制多个传导电子占据每个原子位点。尽管概念上很简单，但该模型提出了困难的计算挑战，即使在二维情况下也是如此。我们模拟联合国小组最近取得的进展，将分析方法和计算方法结合在一个名为“算法松原积分”的过程中，大大减少了计算时间，使得摄动理论中高达六阶的精确结果已经触手可及。本提案旨在完成这一任务。除了二维之外，哈伯德模型已应用于许多系统，特别是那些含有过渡元素或稀土的系统。其中包括金属稀土烧绿石，例如 Pr2Ir2O7；这项工作的长期目标是将我们的数值技术应用于该系统。