ITR: Modeling of Local Critical Behavior in Correlated Electron Systems

该奖项是根据ITR招标（NSF-02-168）提交的“小型”类提案获得的。它支持由局域磁矩和流动电子之间的相互作用引起的新型相关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。通过对模型结果和实验结果的严格比较，PI希望阐明重费米子化合物和高温超导体中相关性的作用。为了实现这些目标，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。在相关电子物理学中，零温度相变在解释高温超导体及其相关材料、重费米子材料和二维电子系统中的非常规金属态中的作用是一个重要的开放性问题。本项目重点研究一类新的量子临界点（QCPs），其中局部自由度的临界波动起着至关重要的作用。这种“局部量子cps”可能是在一些重费米子材料中发现的异常磁有序跃迁，以及高温超导体中非磁性杂质所表现出的磁响应的基础。这项研究的目的是对局部临界波动的物理学有更深的了解，主要是通过使用NRG技术进行计算。拟议的活动有两个主要目标：1。扩展了NRG技术，使扩展的动态平均场近似可以应用于格问题。这将使我们能够获得用微扰方法无法获得的重费米子的Kondo晶格模型的近似解，从而在该模型中建立局部QCP的存在性，并确定该QCP附近的物理性质。为分布式存储机器开发并行NRG算法，以实现涉及大型基集的计算。这种增强的能力将用于研究表现出临界局域矩波动的磁性杂质模型中的局域量子粒子——这些研究本身就很有趣，也将对发展晶格系统的局域临界理论有价值。这些模型将用于计算将非磁性杂质掺杂到d波超导体中所产生的磁性，以便与高tc铜酸盐中杂质的实验进行比较。这项工作不仅可以深入了解杂质的影响，还可以提供有关宿主材料的间接信息。它还将创造新的计算工具，并将其应用于涉及金属和超导体的临界局部矩波动的基本问题。凝聚态理论前沿的研究生和博士后教育将得到加强，并提供先进科学计算方面的培训。本科生将被纳入研究。作为该项目的一部分开发的软件将提供给其他研究人员使用。该合同是根据ITR招标NSF-02-168提交的“小型”类提案授予的。它支持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流动电子之间相互作用的后果，并阐明了电子相关性在重费米子材料和高温超导体中的作用。PI将开发针对并行计算机的新计算算法，以实现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界。该项目还将推进凝聚态理论前沿的研究生和博士后教育，并提供先进科学计算方面的培训。本科生将被纳入研究。作为该项目的一部分开发的软件将提供给其他研究人员使用

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.***