  We consider the U_qSU(2) invariant spin-1/2 XXZ quantum spin chain at roots
of unity q=exp(i*pi/(m+1)), corresponding to different minimal models of
conformal field theory. We conduct a numerical investigation of correlation
functions of U_qSU(2) scalar two-point operators in order to find which
operators in the minimal models they correspond to. Using graphical
representations of the Temperley--Lieb algebra we are able to deal with chains
of up to 28 sites. Depending on q the correlation functions show different
characteristics and finite size behaviour. For m=2/3, which corresponds to the
Lee--Yang edge singularity, we find the surface and bulk critical exponent
-1/5. Together with the known result in the case m=3 (Ising model) this
indicates that in the continuum limit the two-point operators involve conformal
fields of spin (m-1)/(m+1). For other roots of unity q the chains are too short
to determine surface and bulk critical exponents.
