Two-dimensional quantum antiferromagnet with a fourfold degenerate dimer ground state

We study the competition between antiferromagnetic order and valence-bond-crystal formation in a two-dimensional frustrated spin-1/2 model. The J(1)-J(2) model on the square lattice is further frustrated by introducing products of three-spin projectors which stabilize four dimer-product states as degenerate ground state. These four states are reminiscent of the dimerized singlet ground state of the Shastry-Sutherland model. Using exact diagonalization, we study the evolution of the ground state by varying the ratio of interactions. For a large range of parameters (J(2)greater than or similar to 0.25J(1)), our model shows a direct transition between the valence-bond-crystal phase and the collinear antiferromagnetic phase. For small values of J(2), several intermediate phases appear which are also analyzed.