Theoretical Studies of Strongly-Interacting Systems

该项目继续并扩展了与(i)（主要是分数）量子霍尔效应（QHE）和（ii）强量子磁性（主要是反铁磁性）相关的量子强相互作用集体现象的当前研究。这些明显物理上非常不同的强相互作用现象之间令人惊讶的理论联系已经出现，并且将由该项目更充分地探索。将强调新型的非对角线长程序，以及超导氧化物的可能应用。该项目的目标包括：(i)不可压缩分数阶QHE态的更基本分类，（ii）涉及自旋逆转的分数阶QHE态的研究，以及（iii）考虑到有序参数拓扑结构和整数和半整数自旋系统之间的定性差异，发展量子反铁磁性的非线性场论。二维量子自旋系统可能的新“手性”态（即具有破缺反射和时间反转对称性的态）也将被研究。

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.