Frustrated bilayer spin one XY model on the honeycomb lattice

The study of quantum magnetism on geometrically frustrated lattices has been an active field of interest due to the possibility of finding new states of matter such as spin liquids and nematic phases.In this context, honeycomb lattices have attracted a lot of attention due to their interesting and poorly understood magnetic properties.The honeycomb lattice has the lowest value z =3 of the coordination number, leading to a strong effect of quantum fluctuations. In contrat to the spin 1/2 model, not so much theoretical attention has been dedicated to the S = 1 model in spite of its relevance to several materials with spin one. Here I study the spin one bilayer XY antiferromagnet on the honeycomb lattice at zero temperature, with nearest-neighbor J₁ and next-nearest neighbor J₂ exchange interactions and single-ion easy plane anisotropy, using the SU(3) Schwinger boson formalism. The ratio between the interlayer to the intralayer near neighbor exchange interactions exhibits a quantum phase transition at a critical ratio 13.8 that separates the Neel phase from a quantum disordered paramagnetic phase. The effect of next near neighbor interactions is discussed and the phase diagram is presented.