  We obtain the time-dependent correlation function describing the evolution of
a single spin excitation state in a linear spin chain with isotropic
nearest-neighbour XY coupling, where the Hamiltonian is related to the Jacobi
matrix of a set of orthogonal polynomials. For the Krawtchouk polynomial case
an arbitrary element of the correlation function is expressed in a simple
closed form. Its asymptotic limit corresponds to the Jacobi matrix of the
Charlier polynomial, and may be understood as a unitary evolution resulting
from a Heisenberg group element. Correlation functions for Hamiltonians
corresponding to Jacobi matrices for the Hahn, dual Hahn and Racah polynomials
are also studied. For the Hahn polynomials we obtain the general correlation
function, some of its special cases, and the limit related to the Meixner
polynomials, where the su(1,1) algebra describes the underlying symmetry. For
the cases of dual Hahn and Racah polynomials the general expressions of the
correlation functions contain summations which are not of hypergeometric type.
Simplifications, however, occur in special cases.
