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

TL;DR

This study explores the easy-axis Heisenberg model on a triangular lattice, revealing the persistence of certain order parameters across anisotropy regimes and connecting findings to experimental observations of gapped excitations.

Contribution

The paper provides a detailed numerical analysis of excitations and spin structure factors, highlighting the robustness of magnetic order parameters and their relation to experimental materials.

Findings

Robust $m_z$ order parameter across anisotropy regimes

Presence of $m_ot$ order for intermediate anisotropy and magnetic field

Finite magnon excitation gap at small anisotropy, consistent with experiments

Abstract

We investigate the easy-axis Heisenberg model on the triangular lattice by numerically studying excitations and the dynamical spin structure factor $S^{\mu\mu}({\bf q},\omega)$. Results are analyzed within the supersolid scenario, characterized by the translation-symmetry-breaking parameter $m_z$ and the supersolid offdiagonal order parameter $m_\perp$. We find very robust $m_z > 0$ in the whole easy-axis anisotropy regime $\alpha = J_\perp/J_z > 0$, even enhanced by the magnetic field $h>0$, as well as $m_\perp >0$ for intermediate $\alpha <1$ and $h>0$. Still, at small $\alpha \lesssim 0.2$, relevant for recent experiments on the magnetic material K$_2$Co(SeO$_3$)$_2$, we find at $h=0$ rather vanishing $m_\perp \sim 0$, which appears compatible with the numerically established finite magnon excitation gap $\Delta_1 \sim 0.25 \alpha J$.