Union Jack and checkerboard lattices with easy plane single ion anisotropy

The zero-temperature phase diagrams of the antiferromagnetic Union Jack and checkerboard lattices, with spin one and an easy-plane single anisotropy term, are studied using the SU(3) Schwinger boson formalism (also known as flavor wave theory). We find that the Union Jack lattice has a quantum phase transition (QPT) at J2/J1 = 0.707 between a Néel and a collinear phase, while the checkerboard lattice has a QPT at J2/J1 = 0.785, from the Néel to a magnetically disordered phase. The ground state phase diagrams of the two models are different, both from each other and from that of the square lattice antiferromagnet with all the next nearest neighbors. For the checkerboard lattice, we calculate the spin gap and the ground state energy in the disordered phase. This phase is a candidate for a spin liquid state.