Proposal for realizing Heisenberg-type quantum-spin models in Rydberg-atom quantum simulators

We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, $\mathrm{\mid }n{S}_{1\mathrm{/}2},m_J⟩$ and $\mathrm{\mid }(n+1)S_{1\mathrm{/}2},m_J⟩$. In this setting, the effective spin-1/2 Hamiltonian takes the form of an {\it XXZ} model. We show that the anisotropy parameter of the {\it 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.