Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet

Motivated by a recent experimental study on the quantum Ising magnet $\text{K}_2\text{Co}(\text{SeO}_3)_2$ 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 $\omega_n=nJ_{zz}$. Furthermore, we demonstrate the nonlocal multi-spin-flip features for modes at $\omega_2$, indicative of their multi-magnon nature. Additionally, we identify characteristics of the high-field supersolid "$\Psi$" phase in the simulated spectra, which should be compared with future experimental results.