Frustrated spin-1/2 model in two dimensions with columnar dimer states as possible ground states

Abstract

An antiferromagnetic spin S=1/2 model, the J₁-J₂-J₃-J₄-J₅ model, is considered in two dimensions. J₁,J₂,J₃,J₄,J₅ 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 J₁:J₂:J₃:J₄:J₅=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 J₁-J₂-J₃-J₄-J₅ model.