An antiferromagnetic spin S=1/2 model, the ${\mathit{J}}_1$-${\mathit{J}}_2$-${\mathit{J}}_3$-${\mathit{J}}_4$-${\mathit{J}}_5$ model, is considered in two dimensions. ${\mathit{J}}_1$,${\mathit{J}}_2$,${\mathit{J}}_3$,${\mathit{J}}_4$,${\mathit{J}}_5$ are the strengths of the nearest-neighbor, diagonal, next-nearest-neighbor, knight’s-move-distance-away, and further-neighbor-diagonal interactions, respectively. It is known that when ${\mathit{J}}_1$:${\mathit{J}}_2$:${\mathit{J}}_3$:${\mathit{J}}_4$:${\mathit{J}}_5$=1:1:1/2:1/2:1/4 the four columnar dimer states are the exact eigenstates. In a bosonic mean-field theory, we find that the columnar dimer state is the ground state. We compare the results obtained with those obtained in the same mean-field theory for the one-dimensional Majumdar-Ghosh (MG) model. For special values of the couplings, the dimer state is known to be the exact ground state of the MG model. The comparison of the mean-field results for both the models leads to the conjecture that the columnar dimer states are the exact ground states of the ${\mathit{J}}_1$-${\mathit{J}}_2$-${\mathit{J}}_3$-${\mathit{J}}_4$-${\mathit{J}}_5$ model.

• Received 18 May 1995

DOI:https://doi.org/10.1103/PhysRevB.52.12489