Collective Phenomena in Highly Correlated Systems: Quantum Hall Effect and Planar Antiferromagnets

建议进行数值工作，以帮助解决悬而未决的问题 在二维的分数量子化霍尔态中， 强磁场中的电子 这种状态是在 半导体器件和异质结构器件，除了 从应用的角度来看， 理解极端量子极限下的物理现象 合作效应发生的地方。 特别是，该项目 解决问题：非对角线长距离 反向自旋激发及其重要性 甚至分母理性朗道水平的职业; 接近维格纳晶体的经典极限;而且， 无序在分数量子霍尔退化中的作用 states. 还提出了平面反铁磁体的有限尺寸研究 在正方形和三角形格子上。 正方形格子 系统实现在高的氧铜层中， 高温超导体，并被认为是重要的 对超导机制的终极理解。 详细 基态和激发光谱的研究加上 效应和空穴在阻挫模型中的行为 已经提出了次近邻反铁磁耦合。 一 三角波激发谱的并行研究 反铁磁体，其中非常强的量子涨落效应 目前也将进行。

Numerical work is proposed to help resolve outstanding problems in the fractionally quantized Hall states of two-dimensional electrons in strong magnetic fields. Such states are realized in semiconductor MOSFETS and hetrostructure devices which, apart from applied perspective, are valuable testing grounds for the understanding of physical phenomena in the extreme quantum limit where cooperative effects occur. In particular, the project addresses questions on: the off-diagonal long range correlations; the reversed spin excitations and their importance to even denominator rational Landau-level occupations; the approach to the classical limit of a Wigner crystal; and, the role of disorder in degradation of the fractional quantum Hall states. Also proposed is a finite-size study of planar antiferromagnets on both square and triangular lattices. The square lattice systems are realized in the oxygen-copper layers of high temperature superconductors and are deemed important to the ultimate understanding of superconducting mechanism. Detailed studies of the ground state and the excitation spectrum plus the effect and the behavior of holes in the frustrated model with next-neighbor antiferromagnetic coupling have been proposed. A parallel study of the excitation spectrum of the triangular antiferromagnet where very strong quantum fluctuation effects are also present will be carried out.