We study the magnetic-field dependence of the interactions between two alkaline-earth(-like) Rydberg atoms, $\mathrm{Sr}$ and $\mathrm{Yb}$. Considering the pair of Rydberg states $|ns,S_1,m_J\rangle$ and $|(n+1)s,S_1,m_J\rangle$, we show that the effective Hamiltonian takes the form of an XXZ-type quantum spin model, as in the alkali-atom case [M. Kunimi and T. Tomita, Phys. Rev. A 112, L051301 (2025)]. We find that the behavior of the anisotropy parameter for $\mathrm{Yb}$ at zero magnetic field is significantly different from that for other atomic species. This behavior arises from the interplay of strong spin-orbit coupling and the resulting multichannel redistribution of Förster defects in $\mathrm{Yb}$. We systematically calculate the interaction parameters of the XXZ model in the presence of a magnetic field and show that they can be tuned by the field. As applications to quantum many-body problems, we investigate one-dimensional systems in the large-anisotropy regime and show that the folded XXZ model can be realized in $\mathrm{Yb}$ systems without fine-tuning of the field. We also investigate two-dimensional square-lattice systems and show that a supersolid phase can emerge in the ground state at the mean-field level.

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• Quantum simulation
• Rydberg gases
• van der Waals interaction
• Quantum spin models
• Lattice models in condensed matter