DMRG Studies of Doped Antiferromagnets

凝聚态物理学中最令人兴奋的领域之一是研究低维系统中的强关联效应。 特别令人感兴趣的是高温超导铜氧化物。 这些系统表现出广泛的行为，除了超导性，包括反铁磁性和条纹相。 这些系统的模型的数值模拟起着至关重要的作用，因为系统有很强的耦合项和不同类型的顺序之间的竞争。 主要研究者是密度矩阵重整化群（DMRG）的创建者，这是研究强关联系统的最有效技术之一。 本计画将DMRG应用于各种环境下的铜氧化物模型，其中一组研究将探讨二维反铁磁体中超导涡核的性质。 最近的扫描隧道显微镜的研究揭示了有趣的棋盘图案的局部密度的状态周围的涡核，这是尚未了解。 DMRG方法特别适合于研究这种现象。 如果这些模式在模拟中重现，将获得对其起源的清晰理解。 在另一组研究中，将研究铜酸盐常见的铜氧层中掺杂杂质周围的相关性的性质。 这些杂质提供了一个了解这些超导体的正常态的窗口，一个新的技术将被开发用于确定梯形系统的超流刚度和超流密度。 这将提供比通常的配对相关测量更直接的超导信息。 在另一组研究中，我们将研究一种新型的对角取向的梯形系统，以了解二维铜氧层中的节状准粒子。使用另一种数值方法，数值正则变换，我们将从从头计算和更基本的模型中推导出铜氧化物的模型。 目前，模型的构建是一门艺术，而不是一个标准的技术，一个更好的方法可能会揭示现有模型的重要不足之处。本研究过程中开发的算法具有广泛的适用性，可通过互联网访问。%凝聚态物理学中最令人兴奋的领域之一是研究低维系统中的强关联效应。 特别令人感兴趣的是高温超导铜氧化物。 这些系统表现出广泛的行为，除了超导性，包括反铁磁性和条纹相。 这些系统的模型的数值模拟起着至关重要的作用，因为系统有很强的耦合项和不同类型的顺序之间的竞争。 主要研究者是密度矩阵重整化群（DMRG）的创建者，这是研究强关联系统的最有效技术之一。 本项目将DMRG应用于各种情况下的铜酸盐模型。*

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.***