Conformal field theory and the non-abelian SU(2)k chiral spin liquid

Abstract

We construct a family of 1D and 2D long-range SU(2) spin models as parent Hamiltonians associated with infinite dimensional matrix product states that arise from simple current correlation functions in SU(2)k WZW models. Our results provide a conformal field theory foundation for recent proposals by Greiter and coauthors regarding the realization of non-abelian chiral spin liquids. We explain, in particular, how the symmetrization procedure for the amplitudes of the ground state wave function suggested by Greiter M and Thomale R (2009 Phys. Rev. Lett. 102 207203) originates from the conformal field theory description.