Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap

Abstract

To begin with, we introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3bar of SU(3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and hence a Haldane gap in the excitation spectrum. We generalize some of our models to SU(n). Finally, we use the emerging rules for the construction of VBS states to argue that models of antiferromagnetic chains of SU(n) spins in general possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes λwhich is divisible by n. If λand n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If λand n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.

26 pages two-column style, 15 figures, revtex4; references added

References in corpus (11)

• Ultracold fermions and the SU(N) Hubbard model
• Implementation of Spin Hamiltonians in Optical Lattices
• Color Superfluidity and "Baryon" Formation in Ultracold Fermions
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• BCS pairing in Fermi systems with several flavors
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Exact spontaneous plaquette ground states for high-spin ladder models
• SU(N) quantum spin models: A variational wavefunction study
• Ground States of the SU(N) Heisenberg Model
• Statistical Phases and Momentum Spacings for One-Dimensional Anyons
• One-dimensional spin pyrochlore lattice: exact ground state and elementary excitations

Cited by in corpus (8)

• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Simplex solid states of SU(N) quantum antiferromagnets
• DMRG studies of critical SU(N) spin chains
• Entanglement in an SU(n) Valence-Bond-Solid State
• Valence bond solid states with symplectic symmetry
• The matrix product representations for all valence bond states
• Exact models for trimerization and tetramerization in spin chains
• Colored Spin Systems, BKP Evolution and finite N_c effects