ITR: Modeling of Local Critical Behavior in Correlated Electron Systems

该奖项是应国际交易日志征集活动NSF-02-168提交的一个“小”类别提案而颁发的。它支持由局域磁矩和巡回电子之间的相互作用产生的新型关联电子物理的计算和理论研究。PI试图获得对基本模型的理解。通过模型结果和实验之间的关键比较，PI希望阐明关联在重费米子化合物和高温超导体中的作用。为了达到这些目标，数值重整化群(NRG)技术处理磁性杂质问题的能力将得到显著扩展。关联电子物理中一个重要的悬而未决的问题是，零温相变在解释高温超导体及相关材料、重费米子材料和二维电子系统中的非传统金属态方面所起的作用。这个项目关注于一类新的量子临界点(QCP)，在这类临界点上，局部自由度的临界涨落起着至关重要的作用。这种“局域QCP”可能是某些重费密子材料中发现的反常磁序转变的基础，也可能是高温超导体中非磁性杂质表现出磁响应的基础。这项研究的目的是加深对局部临界涨落物理的理解，主要是通过使用NRG技术进行计算。所提出的活动有两个主要推动力：1.扩展NRG技术，使扩展的动力学平均场近似可以应用于晶格问题。这将使得能够获得重费米子的近藤晶格模型的近似解，而该近似解不能通过微扰方法获得，以便在该模型中确定局部QCP的存在，并确定该QCP附近的物理性质。为分布式存储机器的NRG开发并行算法，以实现涉及大基集的计算。这种增强的能力将被用来研究磁杂质模型中的局域QCP，这些模型显示出临界的局域矩涨落--这项研究本身就很有意义，对发展晶格系统的局域临界理论也有价值。这些模型将被用来计算d波超导体中掺杂非磁性杂质所产生的磁性，以便与高T_c铜酸盐中杂质的实验进行比较。这项工作不仅将深入了解杂质的影响，而且还应该提供关于宿主材料的间接信息。它还将导致创建新的计算工具，并将其应用于涉及金属和超导体中关键局部力矩波动的基本问题。将推进凝聚态理论前沿领域的研究生和博士后教育，并提供先进科学计算方面的培训。本科生将被纳入这项研究。作为该项目的一部分而开发的软件将可供其他研究人员使用。%该奖项是在回应ITR征集时提交的一个小类别提案NSF-02-168上颁发的。它支持对相关电子材料的计算和理论研究。研究的重点是局域磁矩和巡回电子之间相互作用的结果，并阐明电子关联在重费米子材料和高温超导体中的作用。PI将开发新的计算算法，目标是并行计算机实现一种被称为数值重整化群的强大方法。由此产生的计算机代码将提供给更广泛的研究社区。该项目还将推进凝聚态理论前沿领域的研究生和博士后教育，并提供先进科学计算方面的培训。本科生将被纳入这项研究。作为该项目的一部分开发的软件将供其他研究人员使用。*

This award was made on a 'small' category proposal submitted in response to the ITR solicitation, NSF-02-168. It supports computational and theoretical research on novel correlated electron physics arising from interactions between localized magnetic moments and itinerant electrons. The PI seeks to gain understanding of fundamental models. Through critical comparison between model results and experiments, the PI hopes to elucidate the role of correlations in heavy-fermion compounds and high-temperature superconductors. To meet these goals, the capabilities of the numerical renormalization group (NRG) technique for treating magnetic impurity problems will be significantly extended. An important open question in correlated electron physics concerns the role of zero-temperature phase transitions in accounting for the unconventional metallic states in high temperature superconductors and related materials, heavy-fermion materials, and two-dimensional electron systems. This project focuses on a novel class of quantum critical points (QCPs) at which critical fluctuations of local degrees of freedom play a crucial role. Such "local QCPs" may underlie the anomalous magnetic ordering transition found in some heavy-fermion materials, as well as the magnetic response exhibited by nonmagnetic impurities in high-temperature superconductors. The aim of the research is to develop a deeper understanding of the physics of local critical fluctuations, primarily through calculations using the NRG technique. The proposed activity has two main thrusts:1. Extend the NRG technique so that the extended dynamical mean-field approximation can be applied to lattice problems. This will enable access to approximate solutions of the Kondo lattice model of heavy fermions that are not accessible from perturbative approaches in order to establish the existence of a local QCP in this model and to determine the physical properties near this QCP.2. Developing parallel algorithms for NRG for distributed memory machines to enable calculations involving large basis sets. This enhanced capability will be used to investigate local QCPs in magnetic impurity models that exhibit critical local-moment fluctuations-studies of interest in their own right that will also be of value in developing theories of local criticality in lattice systems. The models will be used to calculate magnetic properties produced by doping nonmagnetic impurities into d-wave superconductors, permitting comparison with experiments on impurities in high-Tc cuprates. This work will not only yield insight into the effect of the impurities, but should also provide indirect information about the host materials. It will also result in the creation of new computational tools and their application to fundamental problems involving critical local moment fluctuations in metals and superconductors. Graduate and postdoctoral education at the frontiers of condensed matter theory will be advanced and training will be provided in advanced scientific computing. Undergraduates will be integrated into the research. Software developed as part of this project will be made available for use by other researchers.%%%This award was made on a 'small' category proposal submitted in response to the ITR solicitation, NSF-02-168. It supports computational and theoretical research on correlated electron materials. Research focuses on the consequences of interactions between localized magnetic moments and itinerant electrons and elucidating the role of electron correlations in heavy-fermion materials and high temperature superconductors. The PI will develop new computational algorithms targeted for parallel computers to implement a powerful method known as the numerical renormalization group. Resulting computer codes will be made available to the broader research community. The project will also advance graduate and postdoctoral education at the frontiers of condensed matter theory, and provide training in advanced scientific computing. Undergraduates will be integrated into the research. Software developed as part of this project will be made available for use by other researchers.***