Theoretical Studies of Strongly-Interacting Systems

这个项目继续并扩展了当前关于量子强相互作用集体现象的研究，这些现象与(I)(主要是分数级)量子霍尔效应(QHE)和(Ii)强量子磁性(主要是反铁磁性)有关。这些表面上物理上非常不同的强相互作用现象之间惊人的理论联系已经出现，并将在这个项目中得到更充分的探索。新类型的非对角线长程有序将被强调，以及可能的应用于超导氧化物。该项目的目标包括：(I)对不可压缩分数QHE态进行更基本的分类，(Ii)研究涉及自旋反转的分数QHE态，以及(Iii)发展量子反铁磁性的非线性场论，考虑到序参数拓扑以及整数和半整数自旋系统之间的定性差异。我们还将研究2D量子自旋系统中可能出现的新的“手征”态(即具有破裂反射和时间反转对称性的态)。

This project continues and extends current studies of quantum strongly-interacting collective phenomena associated with (i) the (mainly fractional) quantum Hall effect (QHE) and (ii) strongly- quantum magnetism (mainly antiferromagnetism). Surprising theoretical connections between these apparently physically very different strong-interaction phenomena have emerged, and will be more fully explored by this project. Novel types of off-diagonal long-range order will be emphasized, as will the possible application to superconducting oxides. Goals of the project include: (i) a more fundamental classification of incompressible fractional QHE states, (ii) the study of fractional QHE states involving spin-reversal, and (iii) the development of the non- linear field theory of quantum antiferromagnetism, taking into account order-parameter topology and qualitative differences between integer and half-integer spin systmes. Possible novel "chiral" states (i.e., states with broken reflection and time- reversal symmetry) of 2D quantum spin systems will also be investigated.