We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, $|n{S}_{1/2},m_J\rangle$ and $|(n+1)S_{1/2},m_J\rangle$. In this setting, the effective spin-1/2 Hamiltonian takes the form of an XXZ model. We show that the anisotropy parameter of the XXZ model can be tuned by applying a magnetic field and, in particular, that it changes drastically near the Förster resonance points. Based on this result, we propose experimental realizations of spin-1/2 and spin-1 Heisenberg-type quantum spin models in Rydberg atom quantum simulators, without relying on Floquet engineering. Our results provide guidance for future experiments of Rydberg atom quantum simulators and offer insight into quantum many-body phenomena emerging in the Heisenberg model.

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