Easy-axis Heisenberg model on the triangular lattice: from supersolid to gapped solid

We investigate the easy-axis Heisenberg model on the triangular lattice by numerically studying the ground-state dynamical spin structure factor Sμμ( q,ω) on lattices up to $N=36$ sites. Results are analyzed within the supersolid scenario, characterized by the translation-symmetry-breaking parameter mz and the rotational supersolid order parameter m_⊥. We find very robust mz > 0 in the whole easy-axis anisotropy regime α = J_⊥/Jz > 0, even enhanced by the magnetic field $h>0$. Results support also m_⊥ >0 for intermediate α <1 as well as for $h>0$. Still, at small α 1, relevant for recent experiments on the magnetic material K₂Co(SeO₃)₂, we find at $h=0$ rather vanishing m_⊥ ~ 0, reflecting the gapped spin excitations.