Spin wave theory of a one-dimensional generalized Kitaev model

In this work, we perform a combination of classical and spin wave analysis on the one-dimensional spin-$S$ Kitaev-Heisenberg-Gamma model in the region of an antiferromagnetic Kitaev coupling. Four phases are found, including a N\'eel ordered phase, a phase with ${O}_h\ensuremath{\rightarrow}{D}₃$ symmetry breaking, and ``${D}₃$-breaking I, II'' phases which both break ${D}₃$ symmetries albeit in different ways, where ${O}_h$ is the full octahedral group and ${D}₃$ is the dihedral group of order six. The lowest-lying spin wave mass is calculated perturbatively in the vicinity of the hidden SU(2) symmetric ferromagnetic point.