Dimer order with striped correlations in the $J_1{-J}_2$ Heisenberg model

Ground-state energies for plaquette and dimer order in the $J_1{-J}_2$ 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 $J_2{/J}_1,$ where the model is believed to have a quantum disordered ground state. They join smoothly with those obtained from the Ising expansions for the two-sublattice Néel state at $J_2{/J}_1\approx 0.4,$ suggesting a second-order transition from a Néel state to a quantum disordered state, whereas they cross the energy for the four-sublattice ordered state at $J_2{/J}_1\approx 0.6$ at a large angle, implying a first-order transition to the four-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.