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.
