Longitudinal excitations in triangular lattice antiferromagnets

M. Merdan, Y. Xian

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    We study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ (q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We also discuss a possible second longitudinal mode in the triangular lattice model due to the noncollinear nature of its magnetic order.
    Original languageEnglish
    Pages (from-to)797–807
    Number of pages11
    JournalJournal of Low Temperature Physics
    Publication statusPublished - 12 Oct 2012


    • Low-dimensional quantum antiferromagnets
    • Longitudinal excitations
    • Antiferromagnetic Heisenberg model
    • Triangular lattice


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