Spin-1/2 frustrated antiferromagnet on a spatially anisotropic square lattice: Contribution of exact diagonalizations

The phase diagram of a spin-1/2 $J-J^{\prime }-J_2$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the $J_1–J_2$ model on the square lattice with two different nearest-neighbor couplings ${J,J}^{\prime }$ and may also be viewed as an array of coupled Heisenberg chains. The results suggest that the resonating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B 67, 024422 (2003)] for $J_2{=0.5J}^{\prime }\ll J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both sides by a columnar dimer long range order. This columnar order could extend for $J^{\prime }\to J$ which correspond to the $J_1–J_2$ model.