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A 2D quantum antiferromagnet with a four-fold degenerate valence-bond-solid ground state

We study the competition between antiferromagnetic order and valence bond solid formation in a two-dimensional frustrated spin-1/2 model. The J1-J2 model on the square lattice is further frustrated by introducing products of three-spin projectors which stabilize four dimer-product states as degenerate ground states. These four states are reminiscent of the dimerized singlet ground state of the Shastry-Sutherland model. Using exact diagonalizations, we study the evolution of the ground state by varying theratio of interactions. For a large range of parameters (J2 > 0.25J1), our model shows a direct transition between the valence-bond-solid phase and the collinear antiferromagnetic phase. For small values of J2, several intermediate phases appear which are also analyzed.