Strong Correlations in Layered Materials, in Nanoscale Complexes, and in Far-from-Equilibrium Dynamics

层状材料、纳米级复合物和远离平衡动力学中的强相关性

• 批准号: 0605619
• 负责人: John Marston
• 金额: $ 37.8万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605619&HistoricalAwards=false
• 关键词: Strong; Correlations; Layered; Materials; Nanoscale

Technical Summary:The Division of Materials Research and the Division of Mathematical Sciences contribute funding to this award under the NSF-wide Mathematical Sciences Priority Area. This award supports fundamental theoretical research and education in condensed matter physics aimed at a better fundamental understanding of the consequences of strong correlation.Experiments on several classes of layered systems, and on nanoscale aqueous actinide complexes, call for a deeper theoretical understanding of strongly correlated electronic systems. The statistics of dynamical systems such as turbulent flows also require the accurate treatment of strong many-body correlations. The proposed research will employ a combination of systematic analytical and numerical methods to establish phase diagrams, to study charge-transfer at surfaces and in aqueous environments, and to statistically describe nonlinear systems driven out of equilibrium. Three different classes of systems will be investigated:1. Layered materials such as the Cs2CuCl4 and organic k-(BEDT-TTF)2Cu2(CN)3 quantum antiferromagnets, and the Sr14-xCaxCu24O41 ladder materials, exhibit rich behavior characteristic of strongly correlated electronic systems. Antiferromagnetic spin order, spin liquids, gapless deconfined spinon excitations, superconductivity and pseudogap phenomena are either known to occur, or are viable possibilities. Exact diagonalization studies, Gutzwiller variational calculations, renormalization-group and density-matrix renormalization-group calculations, and multi-dimensional bosonization will be used separately, and in combination, to investigate the phase structure of models of the layered materials. The dynamical formation of a Kondo resonance in atom-surface scattering will also be investigated using a systematic truncation of the many-body Hilbert space. Close collaboration with several experimental groups is an important part of this proposed research.2. Actinide ions in aqueous solution disproportionate into multiple oxidation states. The striking degeneracy of the reduction-oxidation potentials suggests that a higher-level organizing principle is at work. This hypothesis is reinforced by the fact that standard density-functional calculations alone are unable to reproduce the degeneracy in the redox potentials. The existence of strong electronic correlations among the 5f electrons may explain this failure. An interdisciplinary project to investigate the physics and chemistry behind actinide disproportionation will be carried out. The possibility that emergent negative-U physics leads to the degeneracy of the redox potentials will be tested by the construction and diagonalization of generalized Hubbard clusters.3. Classical nonlinear dynamical systems such as turbulent flows often exhibit rich behaviors that defy simple explanation. A new approach based upon the Hopf functional method will be used to map the equations of motion for the statistics into a linear framework that resembles quantum mechanics. Techniques borrowed from quantum many-body theory, in particular the powerful flow-equation approach for the renormalization of Hamiltonians, will then be applied. This combined Hopf-Flow approach offers several advantages over past attempts to use renormalization-group ideas in the study of turbulence. To validate the method, comparison will be made with direct numerical simulation.On intellectual grounds, the proposed research will push the boundaries of what can be done to ascertain emergent properties of strongly correlated systems. Gaining a better understanding of this physics is of fundamental importance. This research activity bears on 4 of the 125 outstanding scientific questions identified by Science Magazine in 2005: (1) Is there a unified theory explaining all correlated electron systems? (2) What is the pairing mechanism behind high-temperature superconductivity? (3) What is the structure of water? And (4) Can we develop a general theory of the dynamics of turbulent flows and the motion of granular materials?The proposed work also has several broader impacts. New theoretical tools will be developed and made available to the wider community. Application to the pressing problems of safe storage of actinide nuclear wastes, and to the statistics of geophysical fluid dynamics, important for a better understanding of climate, will be made. Finally, several undergraduates, graduate students, and a postdoc will be trained in cutting-edge methods of theoretical condensed matter physics.Non-Technical Summary:The Division of Materials Research and the Division of Mathematical Sciences contribute funding to this award under the NSF-wide Mathematical Sciences Priority Area. This award supports fundamental theoretical research and education in condensed matter physics aimed at a better fundamental understanding of systems containing electrons or atoms that interact strongly with each other. Strong interactions give rise to correlations in the motions of the constituent particles. In the case of electrons, the PI plans to focus on new phases of mater that can appear in layered materials and the unusual chemistry of actinides, like Neptunium and Plutonium, in water that arise as a consequence of correlations in the motion of electrons. The PI further plans to adapt and extend methods developed for the study of quantum mechanical many particle systems to develop a new approach to the problems of turbulence and fluid flow with potential applications to the study of geophysical fluid dynamics, important for a better understanding of climate.Gaining a better understanding of this physics of strongly correlated systems of particles is of fundamental importance. This research activity bears on 4 of the 125 outstanding scientific questions identified by Science Magazine in 2005: (1) Is there a unified theory explaining all correlated electron systems? (2) What is the pairing mechanism behind high-temperature superconductivity? (3) What is the structure of water? And (4) Can we develop a general theory of the dynamics of turbulent flows and the motion of granular materials?New theoretical tools will be developed and made available to the wider community as a direct consequence of this project. Application to the pressing problems of safe storage of actinide nuclear wastes, and to the statistics of geophysical fluid dynamics will be made. Several undergraduates, graduate students, and a postdoc will benefit from this interdisciplinary project and will be trained in cutting-edge methods of theoretical condensed matter physics.

技术摘要：材料研究部和数学科学部在 NSF 数学科学优先领域为该奖项提供资金。该奖项支持凝聚态物理的基础理论研究和教育，旨在更好地了解强相关性的后果。对几类层状系统和纳米级水性锕系元素络合物的实验要求对强相关电子有更深入的理论理解系统。湍流等动力系统的统计也需要准确处理强多体相关性。拟议的研究将采用系统分析和数值方法相结合来建立相图，研究表面和水环境中的电荷转移，并统计描述失去平衡的非线性系统。将研究三类不同类型的系统：1． Cs2CuCl4和有机k-(BEDT-TTF)2Cu2(CN)3量子反铁磁体和Sr14-xCaxCu24O41梯形材料等层状材料表现出强相关电子系统的丰富行为特征。反铁磁自旋序、自旋液体、无间隙解限自旋子激发、超导性和赝能隙现象要么是已知发生的，要么是可行的可能性。精确对角化研究、Gutzwiller 变分计算、重正化群和密度矩阵重正化群计算以及多维玻色化将单独或组合使用，以研究层状材料模型的相结构。原子表面散射中近藤共振的动态形成也将使用多体希尔伯特空间的系统截断进行研究。与多个实验组的密切合作是本研究的重要组成部分。2．水溶液中的锕系离子歧化成多种氧化态。氧化还原电位的惊人简并性表明更高层次的组织原理正在发挥作用。标准密度泛函计算本身无法重现氧化还原电位的简并性，这一事实强化了这一假设。 5f 电子之间存在强电子相关性可以解释这种失败。将开展一个跨学科项目来研究锕系歧化背后的物理和化学。负U物理导致氧化还原势简并的可能性将通过广义哈伯德团簇的构造和对角化来检验。 3．经典的非线性动力系统（例如湍流）经常表现出丰富的行为，无法简单解释。基于 Hopf 泛函方法的新方法将用于将统计运动方程映射到类似于量子力学的线性框架中。然后将应用从量子多体理论借用的技术，特别是用于哈密顿量重整化的强大流方程方法。与过去在湍流研究中使用重正化群思想的尝试相比，这种组合的 Hopf-Flow 方法具有多种优势。为了验证该方法，将与直接数值模拟进行比较。在知识基础上，拟议的研究将突破确定强相关系统的涌现属性的界限。更好地理解这一物理学至关重要。这项研究活动涉及《科学》杂志2005年确定的125个突出科学问题中的4个：（1）是否存在解释所有相关电子系统的统一理论？ （2）高温超导背后的配对机制是什么？ （3）水的结构是什么？ （4）我们能否发展出湍流动力学和颗粒材料运动的一般理论？所提出的工作还具有一些更广泛的影响。新的理论工具将被开发出来并提供给更广泛的社区。将应用于安全储存锕系核废料的紧迫问题以及地球物理流体动力学统计，这对于更好地了解气候非常重要。最后，几名本科生、研究生和博士后将接受理论凝聚态物理前沿方法的培训。非技术摘要：材料研究部和数学科学部根据 NSF- 为该奖项提供资金广泛的数学科学优先领域。该奖项支持凝聚态物理学的基础理论研究和教育，旨在更好地了解包含彼此强烈相互作用的电子或原子的系统。强相互作用会引起组成粒子运动的相关性。就电子而言，PI 计划重点关注层状材料中可能出现的新物质相，以及水中锕系元素（如镎和钚）的不寻常化学性质，这些化学元素是由于电子运动相关性而产生的。 PI进一步计划调整和扩展为研究量子力学多粒子系统而开发的方法，以开发一种解决湍流和流体流动问题的新方法，并可能应用于地球物理流体动力学的研究，这对于更好地了解气候非常重要更好地理解强相关粒子系统的物理现象至关重要。这项研究活动涉及《科学》杂志2005年确定的125个突出科学问题中的4个：（1）是否存在解释所有相关电子系统的统一理论？ （2）高温超导背后的配对机制是什么？ （3）水的结构是什么？ (4) 我们能否开发出湍流动力学和颗粒材料运动的一般理论？作为该项目的直接结果，我们将开发新的理论工具并将其提供给更广泛的社区。将应用于锕系核废料安全储存的紧迫问题以及地球物理流体动力学统计。一些本科生、研究生和博士后将从这个跨学科项目中受益，并将接受理论凝聚态物理前沿方法的培训。