Abstract
We review recent results obtained for a class of one-dimensional quantum models with $1/r^2$ long-range interaction. Based on the asymptotic Bethe-ansatz solution and conformal field theory, we study critical properties of the continuum boson model, the SU($\nu$) spin chain, the OSp($\nu$,1) supersymmetric {\it t-J} model, and a new hierarchy of models related to the fractional quantum Hall effect. We further investigate the class of $1/r^2$ models with harmonic confinement by means of a newly proposed method of the renormalized-harmonic oscillator solution.
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