Plaquette ordered phase and quantum spin liquid in the spin-1/2 J1-J2 square Heisenberg model*

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions $J_1$ and $J_2$. We use the density matrix renormalization group with implementing $SU(2)$ spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing $J_2$, we find a N\'{e}el phase, a plaquette valence-bond (PVB) phase with a finite spin gap, and a possible spin liquid in a small region of $J_2$ between these two phases. From the finite-size scaling of the magnetic order parameter, we estimate that the N\'{e}el order vanishes at $J_2/J_1\simeq 0.44$. For $0.5 < J_2/J_1 < 0.61$, we find dimer correlations and PVB textures whose decay length grows strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlation function reveals the s-wave character of the PVB order. For $0.44 < J_2/J_1 < 0.5$, both spin and dimer orders are weak on finite-size systems and appear to scale to zero with increasing system width, which is consistent with a possible SL or a near-critical behavior. We compare and contrast our results with earlier numerical studies.