Ground state energies for plaquette and dimer order in the J1−J2 square-lattice spin-half Heisenberg model are compared using series expansion methods. We find that these energies are remarkably close to each other at intermediate values of J2/J1, where the model is believed to have a quantum disordered ground state. They join smoothly with those obtained from the Ising expansions for the 2-sublattice N\'eel-state at J2/J1≈0.4, suggesting a second order transition from a N\'eel state to a quantum disordered state, whereas they cross the energy for the 4-sublattice ordered state at J2/J1≈0.6 at a large angle, implying a first order transition to the 4-sublattice magnetic state. The strongest evidence that the plaquette phase is not realized in this model comes from the analysis of the series for the singlet and triplet excitation spectra, which suggest an instability in the plaquette phase. Thus, our study supports the recent work of Kotov et al, which presents a strong picture for columnar dimer order in this model. We also discuss the striped nature of spin correlations in this phase, with substantial resonance all along columns of dimers.
@article{arxiv.cond-mat/9904064,
title = {Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model},
author = {Rajiv R. P. Singh and Zheng Weihong and C. J. Hamer and J. Oitmaa},
journal= {arXiv preprint arXiv:cond-mat/9904064},
year = {2009}
}