SU(N) Schwinger bosons and nematic phases in the bilinear–biquadratic S=1 triangular lattice antiferromagnet with third-nearest neighbor interactions

•A review of the SU(N) Schwinger boson formalism is presented.•The phase diagram at zero temperature is obtained.•The static and dynamical quadrupolar structure factors are calculated.

I present in details the SU(N) Schwinger boson formalism, also known as flavor wave theory, that has been used several times in the literature. I use the method to study the ferroquadrupolar phase of a quantum biquadratic Heisenberg model with spin S=1 on the triangular lattice with third-nearest-neighbor interactions. Results for the phase diagram at zero temperature and the static and dynamical quadrupolar structure factors are presented. In principle, the results could be applied to NiGa2S4.