DMRG Studies of Doped Antiferromagnets

凝聚态物理中最令人兴奋的领域之一是对低维系统中强相关效应的研究。特别令人感兴趣的是高温超导铜。除了超导性外，这些体系还表现出广泛的行为，包括反铁磁性和条纹相。由于这些系统具有强耦合项和不同阶数之间的竞争，因此系统模型的数值模拟起着至关重要的作用。主要研究者是密度矩阵重整化群（DMRG）的创造者，这是研究强相关系统最有效的技术之一。本项目将DMRG应用于各种情况下的铜模型。在一组研究中，将研究二维反铁磁体中超导涡旋核的性质。最近的扫描隧道显微镜研究揭示了在涡旋核心周围的局部密度状态中有趣的棋盘图案，这些状态尚未被理解。DMRG方法特别适合于研究这种现象。如果在模拟中再现这些模式，就可以清楚地了解它们的起源。在另一组研究中，将研究铜酸盐常见的铜氧层中掺杂杂质的相关性的性质。这些杂质为研究这些超导体的正常状态提供了一个窗口。一种新的超流体刚度和超流体密度测定技术将被开发用于阶梯系统。这将比通常的配对相关测量提供更多关于超导性的直接信息。在另一组研究中，将研究一种新型的对角线定向阶梯系统，以了解二维铜氧层中的节点准粒子。使用另一种数值方法，数值规范变换，我们将从从头计算和更基本的模型中推导出铜的模型。目前，模型的构建是一门艺术，而不是一项标准技术，更好的方法可能会揭示当前模型的重要不足。在本研究过程中开发的算法具有广泛的适用性，并且可以通过互联网访问。凝聚态物理中最令人兴奋的领域之一是对低维系统中强相关效应的研究。特别令人感兴趣的是高温超导铜。除了超导性外，这些体系还表现出广泛的行为，包括反铁磁性和条纹相。由于这些系统具有强耦合项和不同阶数之间的竞争，因此系统模型的数值模拟起着至关重要的作用。主要研究者是密度矩阵重整化群（DMRG）的创造者，这是研究强相关系统最有效的技术之一。本项目将DMRG应用于各种情况下的铜模型

One of the most exciting areas in condensed matter physics is the study of strong correlation effects in low dimensional systems. Of particular interest are the high temperature superconducting cuprates. These systems exhibit a wide range of behavior in addition to superconductivity, including antiferromagnetism and striped phases. Numerical simulations of models of these systems play a crucial role, since the systems have strong coupling terms and competition between different types of order. The principal investigator is the creator of the density matrix renormalization group (DMRG), which is one of the most effective techniques for studying strongly correlated systems. This project will apply DMRG to models of the cuprates in a variety of circumstances.In one set of studies, the properties of a superconducting vortex core in a two-dimensional antiferromagnet will be studied. Recent scanning tunneling microscopy studies have revealed intriguing checkerboard patterns in the local density of states surrounding vortex cores which are not yet understood. The DMRG method id particularly well adapted to study this phenomenon. If these patterns are reproduced in the simulations, a clear understanding will be obtained about their origins. In another set of studies, the nature of the correlations around doped impurities in the copper oxygen layers common to cuprates will be studied. These impurities provide a window into the normal state underlying these superconductors.A novel technique for determining the superfluid stiffness and superfluid density will be developed for ladder systems. This will provide much more direct information about superconductivity than the usual pairing correlation measurements. In another set of studies, a new type of diagonally oriented ladder system will be studied in order to understand nodal quasiparticles in the 2D copper oxygen layers.Using another numerical method, numerical canonical transformations, we will work to derive models for the cuprates from ab initio calculations and from more basic models. Curently, the construction of models is an art rather than a standard technique, and a better method may reveal important inadequacies in current models. Algorithms developed in the course of this research have wide applicability and are accessible via the internet.%%%One of the most exciting areas in condensed matter physics is the study of strong correlation effects in low dimensional systems. Of particular interest are the high temperature superconducting cuprates. These systems exhibit a wide range of behavior in addition to superconductivity, including antiferromagnetism and striped phases. Numerical simulations of models of these systems play a crucial role, since the systems have strong coupling terms and competition between different types of order. The principal investigator is the creator of the density matrix renormalization group (DMRG), which is one of the most effective techniques for studying strongly correlated systems. This project will apply DMRG to models of the cuprates in a variety of circumstances.***