  We propose to use null vectors in conformal field theories to derive model
Hamiltonians of quantum spin chains and corresponding ground state wave
function(s). The approach is quite general, and we illustrate it by
constructing a family of Hamiltonians whose ground states are the chiral
correlators of the SU(2)_k WZW model for integer values of the level k. The
simplest example corresponds to k=1 and is essentially a nonuniform
generalization of the Haldane-Shastry model with long-range exchange couplings.
At level k=2, we analyze the model for N spin 1 fields. We find that the Renyi
entropy and the two-point spin correlator show, respectively, logarithmic
growth and algebraic decay. Furthermore, we use the null vectors to derive a
set of algebraic, linear equations relating spin correlators within each model.
At level k=1, these equations allow us to compute the two-point spin
correlators analytically for the finite chain uniform Haldane-Shastry model and
to obtain numerical results for the nonuniform case and for higher-point spin
correlators in a very simple way and without resorting to Monte Carlo
techniques.
