QUROPE Quantum Information Processing and Communication in Europe

We propose 1D and 2D lattice wave functions constructed from the SU(n)1 Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane-Shastry model as a special case. In 2D, we show that the wave function converges to a class of Halperin multilayer fractional quantum Hall states and belongs to chiral spin liquidsOur result reveals a hidden SU(n) symmetry for this class of Halperin states. When the spins sit on bipartite lattices with alternating fundamental and conjugate representations, we provide numerical evidence that the state in 1D exhibits quantum criticality deviated from the expected behaviors of the SU(n)1 WZW model, while in 2D they are chiral spin liquids being consistent with the prediction of the SU(n)1 WZW model.