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

提出了数值方法来解决二维电子在强磁场中分数量子化霍尔态的突出问题。这种状态是在半导体MOSFET和异质结构器件中实现的，除了应用前景外，它们还是理解发生协同效应的极端量子极限下的物理现象的有价值的测试基础。特别是，该项目解决了以下问题：非对角线长程关联；反向自旋激发及其对偶分母有理Landau能级占据的重要性；接近Wigner晶体的经典极限；以及无序在分数量子霍尔态退化中的作用。还提出了正方形和三角形晶格上平面反铁磁体的有限尺寸研究。正方晶格系统是在高温超导体的氧铜层中实现的，对于最终理解超导机制具有重要意义。详细研究了近邻反铁磁耦合受阻模型中的基态和激发谱以及空穴的作用和行为。同时，还将对具有很强量子涨落效应的三角形反铁磁体的激发光谱进行平行研究。

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.