Spin wave theory of one-dimensional generalized Kitaev model

Abstract

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 $O_h\rightarrow D_3$ 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.