Abstract
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's multilayer fractional quantum Hall states and belongs to chiral spin liquids. Our 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 deviating 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.
Highlights
SU(n) quantum antiferromagnets have been an extensively studied class of strongly correlated systems in condensed matter
In 2D, we find that, on an infinite plane, the wave function converges to a special class of Halperin states that appeared in the context of the multilayer fractional quantum Hall (FQH) effect
In summary, we have constructed a family of spin wave functions with SU(n) symmetry from conformal field theories (CFTs), and we have used the CFT properties of the states to derive parent Hamiltonians in both 1D and 2D
Summary
SU(n) quantum antiferromagnets have been an extensively studied class of strongly correlated systems in condensed matter. Apart from that, for rational CFTs, the existence of null fields allows to derive a (long-range) parent Hamiltonian [56] Following this approach, wave functions have been constructed for the SU(2)k and SO(n) WZW models [56, 59], as well as c = 1 free boson CFTs at particular rational radii [60]. We construct spin wave functions using the SU(n) WZW model and derive parent Hamiltonians of these states in 1D and 2D.
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