 
Summary: 1. Phys. A: Math, Gen. 28 (1995) 35673578. Printed in the UK
Numerical investigation of correlation functions for the
UqSU(2)invariant spin; Heisenberg chain
Peter F Arndt and Thomas Heinzel
PhysikalischesInstitut. Universitu Bonn, NuEallee 12,53115 Bonn, Germany
Received 8 March 1995
AbstracL We consider.the UqSU(2) invariant spin; xxz quantum spin chain at the roots
of unity q = exp(ix/(m i I)), correspondingto different minimal models of conformal field
theory. We conduct a numerical investigation of the correlation functions of UqSU(2)scalar
twopointoperators in order to find which operatorsin theminimal models they correspond to.
Using graphical representationsof the TemperleyLieb algebra we are able to deal with chains
of up to 28 sites. Dependingon q. the correlation functions show differentcharacteestics and
finitesize behaviour. For m = 213, which correspondsto the LYang edge singularity, we
find the surface and bulk critical exponent 1j5. Together with the known result in the case
m =3 (king model) this indicates that in the continuum limit the tWOpOint operators involve
conformal fields of s p i n  s . For other roo$ of unity q the.&ains are too short to determine
thesurface and bulk uitical exponents.
1. Introduction
We considertwopoint correlation functions for a class of onedimensionalquantum models
on a chain of N sites defined in terms of the Hamiltonian [1,2]
