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

技术摘要：材料研究部和数学科学部在nsf数学科学优先领域下为该奖项提供资金。该奖项支持凝聚态物理的基础理论研究和教育，旨在更好地理解强相关性的后果。在几类层状系统和纳米级水系锕系络合物上的实验，要求对强相关电子系统有更深的理论理解。诸如紊流等动力系统的统计也需要对强多体相关性进行精确处理。拟议的研究将采用系统分析和数值方法的结合来建立相图，研究表面和水环境中的电荷转移，并统计地描述非线性系统被赶出平衡。我们将研究三种不同类型的系统：层状材料如Cs2CuCl4和有机k-(BEDT-TTF)2Cu2(CN)3量子反铁磁体，以及Sr14-xCaxCu24O41阶梯材料，表现出丰富的强相关电子系统行为特征。反铁磁自旋有序、自旋液体、无间隙自旋激振、超导性和赝隙现象要么已知发生，要么是可行的。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子化将分别或结合使用来研究层状材料模型的相结构。使用多体希尔伯特空间的系统截断，还将研究原子表面散射中近道共振的动力学形成。与几个实验小组的密切合作是本研究的重要组成部分。锕系离子在水溶液中不成比例地形成多种氧化态。还原氧化电位的显著退化表明，有更高层次的组织原理在起作用。标准的密度泛函计算不能再现氧化还原电位的简并，这一事实加强了这一假设。5f电子之间强电子相关性的存在可以解释这种失败。一个跨学科的项目，以调查背后的物理和化学锕歧化将进行。突发性负u物理导致氧化还原电位简并的可能性将通过广义Hubbard簇的构建和对角化来检验。经典的非线性动力系统，如湍流，往往表现出难以简单解释的丰富行为。一种基于Hopf泛函方法的新方法将被用于将统计运动方程映射到类似量子力学的线性框架中。从量子多体理论中借鉴的技术，特别是用于哈密顿量重整化的强大的流动方程方法，将被应用。这种组合的Hopf-Flow方法比过去在湍流研究中使用重整化群思想的尝试有几个优点。为了验证该方法，将与直接数值模拟进行比较。从知识的角度来看，拟议的研究将突破确定强相关系统的涌现特性的界限。更好地理解这种物理学是至关重要的。这项研究活动涉及2005年《科学》杂志确定的125个突出科学问题中的4个：(1)是否存在一个统一的理论来解释所有相关的电子系统？(2)高温超导的配对机制是什么？(3)水的结构是什么？(4)我们能否发展出紊流动力学和粒状物质运动的一般理论？拟议的工作也有几个更广泛的影响。新的理论工具将被开发并提供给更广泛的社区。将应用于锕系核废料的安全贮存这一紧迫问题，以及对更好地了解气候很重要的地球物理流体动力学统计。最后，几名本科生、研究生和一名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在nsf数学科学优先领域下为该奖项提供资金。该奖项支持凝聚态物理的基础理论研究和教育，旨在更好地理解包含电子或原子的系统，这些系统相互作用强烈。强相互作用使组成粒子的运动产生相互关系。就电子而言，PI计划将重点放在可以出现在分层材料中的物质的新相，以及锕系元素（如镎和钚）在水中的不寻常化学反应上，这些化学反应是电子运动相关的结果。PI进一步计划调整和扩展用于研究量子力学的许多粒子系统的方法，以开发一种新的方法来研究湍流和流体流动问题，并有可能应用于地球物理流体动力学的研究，这对更好地理解气候很重要。更好地理解这种强相关粒子系统的物理学是至关重要的。这项研究活动涉及2005年《科学》杂志确定的125个突出科学问题中的4个：(1)是否存在一个统一的理论来解释所有相关的电子系统？(2)高温超导的配对机制是什么？(3)水的结构是什么？(4)我们能否发展出紊流动力学和粒状物质运动的一般理论？作为这个项目的直接结果，新的理论工具将被开发出来并提供给更广泛的社区。应用于锕系核废料安全贮存的迫切问题，以及地球物理流体动力学的统计。几名本科生、研究生和一名博士后将从这个跨学科项目中受益，并将在理论凝聚态物理的前沿方法方面接受培训。

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.