FRUSTRATED SPIN-1/2 MODEL IN 2 DIMENSIONS WITH COLUMNAR DIMER STATES AS POSSIBLE GROUND-STATES

An antiferromagnetic spin S = 1/2 model, the J(1)-J(2)-J(3)-J(4)-J(5) model, is considered in two dimensions. J(1),J(2),J(3),J(4),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 J(1):J(2):J(3):J(4):J(5)=1:1:1/2:1/2:1/4 the four columnar dimer states are the exact eigenstates. In a bosonic mean-held 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 J(1)-J(2)-J(3)-J(4)-J(5) model.