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We propose to use null vectors in conformal field theories to derive modelHamiltonians of quantum spin chains and corresponding ground state wavefunction(s). The approach is quite general, and we illustrate it byconstructing a family of Hamiltonians whose ground states are the chiralcorrelators of the SU(2)_k WZW model for integer values of the level k. Thesimplest example corresponds to k=1 and is essentially a nonuniformgeneralization 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 Renyientropy and the two-point spin correlator show, respectively, logarithmicgrowth and algebraic decay. Furthermore, we use the null vectors to derive aset of algebraic, linear equations relating spin correlators within each model.At level k=1, these equations allow us to compute the two-point spincorrelators analytically for the finite chain uniform Haldane-Shastry model andto obtain numerical results for the nonuniform case and for higher-point spincorrelators in a very simple way and without resorting to Monte Carlotechniques.

Quantum spin Hamiltonians for the SU(2)_k WZW model