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Anisotropic Heisenberg model close to the Ising limit: Triangular lattice versus effective models

M. Ulaga1,*, J. Kokalj2,3, T. Tohyama4, and P. Prelovšek3

  • *Contact author: martinu@pks.mpg.de
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Phys. Rev. B 114, 034411 – Published 8 July, 2026

DOI: https://doi.org/10.1103/f5xy-9q3m

Abstract

Stimulated by recent experiments on materials representing the realization of the anisotropic Heisenberg spin-1/2 model on a triangular lattice (TL), we explore further properties of such a model in the easy-axis regime α=J⊥/Jz<1 and the plausibility of finding effective models that capture similar physics. We show that, at finite fields, the magnetization curve as well as the transverse magnetization (superfluid) order parameter m⊥ of the TL model are indeed qualitatively reproduced by anisotropic Heisenberg models on the honeycomb or square lattice. At the point of correspondence to the zero-field TL model, however, the bipartite models are qualitatively different, as they remain gapless even at α≪1 with a small but finite m⊥>0. Conversely, we present several additional numerical studies of the full model on the TL which support the appearance of a gap at zero field and α≪1. The magnetization curve m(h) and the spin stiffness ρs indicate a transition/crossover from gappless to gapped regimes at α∼α*, with α*≲0.5. We also show that deviations from the linear spin-wave theory and the emergence of the gap can be traced back to the strong effective repulsion between magnon excitations, showcasing similarity to strongly correlated systems.

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Phys. Rev. B 114, 034411– Published 8 July, 2026
  • Received 14 October 2025
  • Revised 3 January 2026
  • Accepted 12 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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