Fourfold degenerate columnar-dimer ground state in square lattice antiferromagnets

We construct and study the two frustrated quantum spin-1∕2 models on square lattice, which are like the antiferromagnetic J₁-J₂ model with some additional four-spin exchange interactions. These models admit an exactly solvable case in which the ground state consists of four degenerate columnar-dimer singlet (CDS) configurations. Away from the exact case, we employ bond-operator mean-field theory to investigate the evolution of the ground state by varying the interaction parameters. The mean-field calculation reveals a quantum phase diagram in which the CDS phase undergoes a continuous phase transition to either Néel or collinear ordered antiferromagnetic phases.