Theory of Quantum Antiferromagnets

本文将对这部小说进行全面的理论研究 受抑、掺杂和随机量子的性质 反铁磁体 最近的非弹性中子散射测量 为我们提供了大量关于自旋动力学的信息 掺杂的铜酸盐：一个成功的解开的性质， 自旋涨落对于更深入地理解 这些高温超导体的新特性。 为了理解这些测量，我们将研究 二维反铁磁体的普适性质 在零温度相变附近， 范围磁序消失。 掺杂的影响，淬火 随机性、无公度自旋涨落和初始相位 这种相变和量子无序的分离 阶段将进行检查。 其他受挫的层状反铁磁体 近年来也进行了研究：特别是， 晶格是一个强有力的，实验上可实现的候选者， 显示出无序的基态。 我们将承担一个 这些系统的理论研究：量子相位的性质 反铁磁体的相变和量子无序相 在二维格阻上的对偶性将被研究 分析和映射到二聚体模型。 最后，低 金属和绝缘材料的温度磁性能 将研究掺杂半导体的相：这些材料是 很好地描述了一个强随机哈伯德模型， 通过数值和分析方法进行研究。 %%% 理论研究将进行磁模型， 在与强相互作用的物理相关的问题的核心， 例如高温超导体。 这些 问题是目前研究的最前沿， 物质物理学

A comprehensive theoretical study will be made of the novel properties of frustrated, doped, and random quantum antiferromagnets. Recent inelastic neutron scattering measurements have provided us with a wealth of information on the spin dynamics of the doped cuprates: a successful unraveling of the nature of the spin fluctuations is clearly important to a deeper understanding of the novel properties of these high temperature superconductors. With the aim of understanding these measurements, we will study the universal properties of two-dimensional antiferromagnets in the vicinity of a zero temperature phase transition at which the long- range magnetic order vanishes. The effects of doping, quenched randomness, incommensurate spin fluctuations, and incipient phase separation on this phase transition and the quantum disordered phase will be examined. Other frustrated, layered antiferromagnets have also been studied in recent years: in particular, the kagome lattice is a strong, experimentally realizable candidate for displaying a disordered ground state. We will undertake a theoretical study of these systems: the nature of quantum phase transitions and the quantum disordered phases of antiferromagnets on frustrated two-dimensional lattices will be studied by a duality analysis and mappings to dimer models. Finally, the low temperature magnetic propoerties of the metallic and insulating phases of doped semiconductors will be studied: these materials are well described by a strongly random Hubbard model which will be examined by numerical and analytic approaches. %%% Theoretical research will be conducted on magnetic models which are at the core of problems related to strongly interacting physical systems such as the high temperature superconductors. These problems are at the forefront of present research in condensed matter physics.