Critical Properties of Quantum Many-Body Systems with 1/r^2 Interaction
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(
ν
) spin chain, the OSp(
ν
,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.