We show that the chiral correlators of the SU(2) level k WZW model can be used as ground states of quantum spin chains. Employing the null vectors of this Rational CFT, we construct the corresponding Hamiltonians. At level k=1 we recover the Haldane-Shastry spin chain which is generalized to study dimerized and random chains. At level k=2 we construct a spin 1 chain whose ground state is a pfaffian, and a spin 1/2 chain whose ground state is degenerate, according to the fusion rules of the WZW. These models are further generalized to two dimensions. We shall also briefly discuss the relation with the Fractional Quantum Hall wave functions allowing for topological quantum computation.
Joint ICTP/SISSA Statistical Physics seminar: "Quantum spin Hamiltonian for the SU(2) Wess-Zumino-Witten model"
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