Theory of Quantum Antiferromagnets

对受挫、掺杂和随机量子反铁磁体的新特性进行了全面的理论研究。最近的非弹性中子散射测量为我们提供了关于掺杂铜酸盐的自旋动力学的丰富信息：成功地揭示自旋涨落的性质显然对更深入地理解这些高温超导体的新特性很重要。为了理解这些测量结果，我们将研究二维反铁磁体在零温度相变附近的普遍性质，在此相变处，长程磁序消失。研究了掺杂、猝灭随机性、不相称自旋涨落和初始相分离对相变和量子无序相的影响。近年来，其他受挫的层状反铁磁体也得到了研究：特别是，kagome晶格是显示无序基态的一个强大的、实验上可实现的候选。我们将对这些系统进行理论研究：将通过对偶分析和映射到二聚体模型来研究受挫二维晶格上反铁磁体的量子相变和量子无序相的性质。最后，将研究掺杂半导体的金属相和绝缘相的低温磁性能：这些材料由强随机哈伯德模型很好地描述，并将通过数值和解析方法进行检验。将对磁性模型进行理论研究，这是与强相互作用物理系统（如高温超导体）相关问题的核心。这些问题是当前凝聚态物理研究的前沿。

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.