Density Matrix Renormalization Group Studies of Frustrated and Doped Systems

受阻和掺杂系统的密度矩阵重整化群研究

• 批准号: 0907500
• 负责人: Steven White
• 金额: $ 47.5万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0907500&HistoricalAwards=false
• 关键词: Density; Matrix; Renormalization; Group; Studies

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). TECHNICAL SUMMARYThis grant supports theoretical research on the properties of strongly interacting electron systems in low dimensions. In particular, the research focuses on the application of the density-matrix renormalization group (DMRG) method, developed by the PI in 1992, to several relevant problems of strongly correlated electrons. This method is one of the most reliable and now widely used techniques to treat strong correlations and quantum systems, and has been extended to several other areas in materials theory. The study of strong correlation effects in low dimensional systems is one of the most exciting areas in condensed matter physics. These systems exhibit a wide range of behavior, such as high temperature superconductivity, antiferromagnetism, striped, and spin liquid phases. Numerical simulation techniques have become increasingly necessary to understand these systems, as the systems have strong coupling terms and competition between different types of order. This research will develop improved methods for describing transport and consequently being able to compare theory with experiment. For example, recent breakthroughs in real-time DMRG will allow the study of spectral functions for a variety of chain, ladder, and small 2D cluster systems. The PI anticipates being able to calculate temperature-dependent dynamical properties of 2D copper-oxygen plane models which can be compared directly with scanning tunneling microscopy (STM) experiments. The development of methods for simulating 2D doped and frustrated systems will also be pursued, using both traditional 2D DMRG "wide ladders" and novel algorithms based on tensor networks. Two-dimensional models for cuprate superconductors and recently discovered Fe-superconductors will be studied using large 2D clusters.Another important component of this research will be the development of a general purpose software library for matrix computations used within DMRG simulations, which will be made freely available to other researchers.NONTECHNICAL SUMMARYThis grant supports primarily computational research on the properties of strongly interacting systems of electrons in one- and two-dimensions, with particular application to nanodevices and superconducting materials. The behavior of electrons when they are confined in these small spaces and when they are very close to each other can lead to novel effects. This grant supports work that will develop computational techniques to describe these effects. In addition to discovering and understanding novel properties, which may lead to new devices, the computational techniques developed will find wide application in other fields of study. This is the power of developing computational methods in one field that can be applied to many other applications. Students involved in this research will receive excellent training in condensed matter physics and computational physics.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。技术概述：本基金支持低维强相互作用电子系统性质的理论研究。重点研究了PI于1992年提出的密度矩阵重整化群（DMRG）方法在强相关电子若干相关问题中的应用。这种方法是目前广泛应用于处理强相关和量子系统的最可靠的技术之一，并已扩展到材料理论的其他几个领域。低维系统中强相关效应的研究是凝聚态物理中最令人兴奋的领域之一。这些体系表现出广泛的行为，如高温超导、反铁磁性、条纹和自旋液相。数值模拟技术对于理解这些系统变得越来越必要，因为这些系统具有强耦合项和不同类型顺序之间的竞争。这项研究将改进描述输运的方法，从而能够将理论与实验进行比较。例如，实时DMRG的最新突破将允许研究各种链状、阶梯状和小型二维星团系统的光谱函数。PI期望能够计算二维铜氧平面模型的温度相关动力学特性，这可以直接与扫描隧道显微镜（STM）实验进行比较。研究人员还将利用传统的二维DMRG“宽阶梯”和基于张量网络的新算法，开发模拟二维掺杂和受挫系统的方法。铜超导体和最近发现的铁超导体的二维模型将使用大型二维簇进行研究。这项研究的另一个重要组成部分将是开发用于DMRG模拟中矩阵计算的通用软件库，该软件库将免费提供给其他研究人员。该基金主要支持一维和二维强相互作用电子系统特性的计算研究，特别是纳米器件和超导材料的应用。当电子被限制在这些小空间中时，当它们彼此非常接近时，它们的行为会导致新的效应。这项拨款支持将开发计算技术来描述这些影响的工作。除了发现和理解可能导致新设备的新特性外，所开发的计算技术还将在其他研究领域得到广泛应用。这是在一个领域开发计算方法的力量，它可以应用于许多其他应用。参与本研究的学生将接受凝聚态物理和计算物理方面的优秀培训。