On the two-point correlation functions for the Uq[SU(2)]invariant spin one-half Heisenberg chain at roots of unity

Using Uq[SU(2)] tensor calculus we compute the two-point scalar operators (TPSO), their averages on the ground-state give the two-point correlation functions. The TPSOs are identified as elements of the Temperley-Lieb algebra and a recurrence relation is given for them. We have not tempted to derive the analytic expressions for the correlation functions in the general case but got some partial results. For q=eiπ/3, all correlation functions are (trivially) zero, for q=eiπ/4, they are related in the continuum to the correlation functions of left-handed and right-handed Majorana fields in the half plane coupled by the boundary condition. In the case q=eiπ/6, one gets the correlation functions of Mittag's and Stephen's parafermions for the three-state Potts model. A diagrammatic approach to compute correlation functions is also presented. (orig.)