Motivated by a recent experimental study on the quantum Ising magnet ${\text{K}}_2\text{Co}{\left({\text{SeO}}_3\right)}_2$ that presented spectroscopic evidence of zero-field supersolidity (Chen et al., arXiv:2402.15869), we simulate the excitation spectrum of the corresponding microscopic $XXZ$ model for the compound using the recently developed excitation ansatz for infinite projected entangled-pair states. We map out the ground state phase diagram and compute the dynamical spin structure factors across a range of magnetic field strengths, focusing especially on the two supersolid phases found near zero and saturation fields. Our simulated excitation spectra for the zero-field supersolid “Y” phase are in excellent agreement with the experimental data, recovering the low-energy branches and integer quantized excited energy levels ${\omega }_n=n{J}_{zz}$. Furthermore, we demonstrate the nonlocal multi-spin-flip features for modes at ${\omega }_2$, indicative of their multimagnon nature. Additionally, we identify characteristics of the high-field supersolid “$\mathrm{\Psi }$” phase in the simulated spectra, which should be compared with future experimental results.

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• Spin dynamics
• Antiferromagnets
• Supersolids
• Triangular lattice
• Tensor network methods