Photon- and roton-like excitations of the triangular lattice XXZ supersolid

Motivated by recent experiments, we investigate the spin-1/2 XXZ model on the triangular lattice with strong Ising anisotropy, combining large-scale numerical simulations and analytical methods to uncover unconventional spin dynamics. First, we compute the dynamical spin structure factor using density matrix renormalization group (DMRG) simulations and find excellent agreement with inelastic neutron scattering data on the layered compound $\text{K}_2\text{Co}(\text{SeO}_3)_2$. The low-energy spectrum reveals a roton-like minimum at the $M$ point—absent in linear spin-wave theory—accompanied by peak intensity and a broad continuum above it. Near the $\Gamma$ point, we observe an approximately linear dispersion with vanishing spectral weight. Second, we compare two analytical frameworks that reproduce the observed features. The first is a hard-core boson approach, which includes: (i) an effective staggered boson model (ESBM) at zero magnetic field, (ii) perturbation theory applied to the one-third magnetization plateau, and (iii) a self-consistent mean-field Schwinger boson theory (SBT). The second framework is based on a variational supersolid quantum dimer model (QDM) ansatz, combined with a single-mode approximation. The SBT captures the broad continuum, the $M$-point minimum, and linear dispersion at $\Gamma$, whereas the QDM reproduces the roton minimum and linear dispersion at finite momentum near $\Gamma$. Remarkably, both the QDM wavefunction and the DMRG ground state exhibit nearly identical structure factors with pronounced transverse photon-like excitations. Together, our comprehensive theoretical and numerical analysis elucidates the microscopic origin of supersolid excitations in the XXZ triangular lattice model and their proximity to a spin liquid phase observed experimentally.