Prototypical models and their material incarnations are cornerstones to the understanding of quantum magnetism. Here we show theoretically that the recently synthesized magnetic compound Na₂BaCo(PO₄)₂ (NBCP) is a rare, nearly ideal material realization of the S = 1/2 triangular-lattice antiferromagnet with significant easy-axis spin exchange anisotropy. By combining the automatic parameter searching and tensor-network simulations, we establish a microscopic model description of this material with realistic model parameters, which can not only fit well the experimental thermodynamic data but also reproduce the measured magnetization curves without further adjustment of parameters. According to the established model, the NBCP hosts a spin supersolid state that breaks both the lattice translation symmetry and the spin rotational symmetry. Such a state is a spin analog of the long-sought supersolid state, thought to exist in solid Helium and optical lattice systems, and share similar traits. The NBCP therefore represents an ideal material-based platform to explore the physics of supersolidity as well as its quantum and thermal melting.

原型模型及其材料化身是理解量子磁学的基石。在这里，我们从理论上证明，最近合成的磁性化合物 Na ₂ BaCo(PO ₄ ) _{2 (NBCP) 是一种罕见的、近乎理想的}S材料实现。 = 1/2 具有显着易轴自旋交换各向异性的三角晶格反铁磁体。通过结合自动参数搜索和张量网络模拟，我们建立了具有真实模型参数的该材料的微观模型描述，不仅可以很好地拟合实验热力学数据，而且无需进一步调整参数即可再现测量的磁化曲线。根据已建立的模型，NBCP 拥有一个自旋超固态，它打破了晶格平移对称性和自旋旋转对称性。这种状态是长期寻找的超固态的自旋类似物，被认为存在于固态氦和光学晶格系统中，并且具有相似的特征。