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

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 ⊥ / J z < 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 ρ s 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.