We study the nature of the ground state of the frustrated J₁-J₂ model and the J₁-J₃ model using a variational algorithm based on projected entangled pair states. By investigating spin-spin correlation functions, we observe a separation in parameter regions with long- and short-range order. A direct comparison with exact diagonalizations in the subspace of short-range valence bond singlets reveals that the system is well described by states within this subset in the short-range order regions. We discuss the question whether the system forms a spin liquid, a plaquette valence bond crystal, or a columnar dimer crystal in these parameter regions.
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Murg et al. (2009) studied this question.
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