Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model

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.

28 pages, 9 figures, published version

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Cited by in corpus (14)

• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Full counting statistics in the Haldane-Shastry chain
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Infinite Matrix Product States for long range SU(N) spin models
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Excited States in Spin Chains from Conformal Blocks
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Entanglement properties of the two-dimensional SU(3) AKLT state
• The BCS wave function, matrix product states, and the Ising conformal field theory
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains