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

Martin Greiter and Stephan Rachel
Phys. Rev. B 75, 184441 – Published 31 May 2007

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 λ which is divisible by n. If λ and n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If λ and n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.

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  • Received 19 January 2007

DOI:https://doi.org/10.1103/PhysRevB.75.184441

©2007 American Physical Society

Authors & Affiliations

Martin Greiter and Stephan Rachel

  • Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, Postfach 6980, 76128 Karlsruhe, Germany

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Issue

Vol. 75, Iss. 18 — 1 May 2007

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