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

doi:https://doi.org/10.1103/PHYSREVB.75.184441

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

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Abstract

To begin with, we introduce several exact models for SU(3) spin chains: First is a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3 of SU(3) if the original spins of the model transform under representation 3. Second is a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin representations 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 valence bond solid 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 {lambda} which is divisible by n. If {lambda} and n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If {lambda} and n have a common divisor differentmore »« less

Authors:

Greiter, Martin; Rachel, Stephan ^[1]

Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, Postfach 6980, 76128 Karlsruhe (Germany)

Publication Date:: 2007-05-01

OSTI Identifier:: 20951418

Resource Type:: Journal Article

Journal Name:: Physical Review. B, Condensed Matter and Materials Physics

Additional Journal Information:: Journal Volume: 75; Journal Issue: 18; Other Information: DOI: 10.1103/PhysRevB.75.184441; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; ANTIFERROMAGNETISM; CHAINS; CONFINEMENT; EXCITATION; GROUND STATES; HAMILTONIANS; SOLIDS; SPIN; SU-3 GROUPS; VALENCE

Citation Formats


                    Greiter, Martin, and Rachel, Stephan. Valence bond solids for SU(n) spin chains: Exact models, spinon confinement, and the Haldane gap.  United States: N. p., 2007. 
        Web.  doi:10.1103/PHYSREVB.75.184441.

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                    Greiter, Martin, & Rachel, Stephan. Valence bond solids for SU(n) spin chains: Exact models, spinon confinement, and the Haldane gap.  United States.  https://doi.org/10.1103/PHYSREVB.75.184441

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                    Greiter, Martin, and Rachel, Stephan. Tue .  
        "Valence bond solids for SU(n) spin chains: Exact models, spinon confinement, and the Haldane gap".  United States.  https://doi.org/10.1103/PHYSREVB.75.184441.

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@article{osti_20951418,

  title        = {Valence bond solids for SU(n) spin chains: Exact models, spinon confinement, and the Haldane gap},

  author       = {Greiter, Martin and Rachel, Stephan},

  abstractNote = {To begin with, we introduce several exact models for SU(3) spin chains: First is a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3 of SU(3) if the original spins of the model transform under representation 3. Second is a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin representations 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 valence bond solid 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 {lambda} which is divisible by n. If {lambda} and n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If {lambda} and n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.},

  doi          = {10.1103/PHYSREVB.75.184441},

  url          = {https://www.osti.gov/biblio/20951418},
  journal      = {Physical Review. B, Condensed Matter and Materials Physics},

  issn         = {1098-0121},

  number       = 18,

  volume       = 75,

  place        = {United States},

  year         = {2007},

  month        = {5}

}

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