Frustrated quantum antiferromagnet with third neighbor interactions and single ion anisotropy on the honeycomb lattice

•We use the SU(3) Schwinger boson formalism.•We present the phase diagram at zero temperature.•We calculate the gap in the disordered phase.

I study the spin-1 Heisenberg antiferromagnet on the two dimensional honeycomb lattice at zero temperature, with first J1, second J2 and third J3 neighbors exchange interactions and single ion easy plane anisotropy, using the SU(3) Schwinger boson formalism. The phase diagram is shown. The results show the existence of a region in the intermediate frustrated regime where the system does not have quantum magnetic order.