Anisotropic-exchange magnets on a triangular lattice: spin waves and accidental degeneracies

We present an overview of the phase diagram, spin-wave excitations, and finite-temperature transitions of the anisotropic-exchange magnets on a nearest-neighbor triangular lattice. We investigate transitions between five principal classical phases: ferromagnetic, Néel, its dual, and the two stripe phases. Transitions are identified by the spin-wave instabilities and by the Luttinger-Tisza approach. In the stripe phases, quantum fluctuations are mostly negligible, leaving the ordered moment nearly saturated even for S = 1/2. However, for a 2D surface of the full 3D parameter space, the spin-wave spectrum in one of the stripe phases exhibits an accidental degeneracy. As a result, the ordering transition temperature in a wide region of the phase diagram is suppressed. This accidental degeneracy is due to a correspondence to an extended Kitaev-Heisenberg model with emergent symmetries.