Magnetic excitations of the strongly-anisotropic triangular XXZ model: a projected spin-product state approach

Recent experiments have sparked interest on the ground-state properties and on the excitation spectrum of the spin-$1\mathrm{/}2$ triangular XXZ model with strong Ising-like anisotropy. In this work, we introduce and analyze a ``projected’’ coherent-state approximation to the model, constructed by projecting spin-product states onto the low-energy configurations of the triangular Ising antiferromagnet. Within this approximation, we discuss the structure of the ground-state ordering and the magnetization curve under a longitudinal field. We then discuss the excitation spectrum by linearizing equations of motion deriving from a time-dependent variational principle. This leads to a natural description of spin-wave-like excitations within the strongly constrained Hilbert space. At zero field, the variational approximation leads to a very flat landscape of quasi-degenerate states, which results in a low-energy pseudo-Goldstone mode in the excitation spectrum. We compare our results to experimental measurements on the cobaltite K${}_2$Co(SeO${}_3$)${}_2$ (KCSO). Our approximation leads to a dramatic improvement as compared to linear spin-wave theory. However, there remain deviations in the value of the pseudo-Goldstone gap and in the dispersion near $M$ points at low field.