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

Martin Ulaga, Jure Kokalj, Peter Prelovšek
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Abstract

We investigate the easy-axis Heisenberg model on the triangular lattice by numerically studying the ground-state dynamical spin structure factor $S^{\mu\mu}({\bf q},\omega)$ on lattices up to $N=36$ sites. Results are analyzed within the supersolid scenario, characterized by the translation-symmetry-breaking parameter $m_z$ and the rotational supersolid 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 $h>0$. Results support also $m_\perp >0$ for intermediate $\alpha <1$ as well as for $h>0$. Still, at small $\alpha \ll 1$, relevant for recent experiments on the magnetic material K$_2$Co(SeO$_3$)$_2$, we find at $h=0$ rather vanishing $m_\perp \sim 0$, reflecting the gapped spin excitations.
三角形晶格上的易轴海森堡模型:从超固体到间隙固体
我们研究了三角形晶格上的易轴海森堡模型,通过数值研究了晶格上高达 $N=36$ 位点的基态动态自旋结构因子$S^{\mu\mu}({\bf q},\omega)$。我们在超固态情景下对结果进行了分析,超固态情景以平移对称性破坏参数$m_z$和旋转超固态阶参数$m_\perp$为特征。我们发现在整个易轴各向异性机制中,$m_z>0$是非常稳健的,甚至在磁场$h>0$的作用下还会增强。对于中间的 $\alpha 0$,结果也支持 $m_\perp>0$。不过,在小$α \ll 1$(与最近在磁性材料K$_2$Co(SeO$_3$)$_2$上的实验有关)时,我们发现在$h=0$时$m_perp \sim 0$反而消失了,这反映了间隙自旋激发。
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