Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J_1−J_2 Square Heisenberg Model

Abstract

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J_1 and J_2, which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z_2 spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU (2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J_2 , we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J_2 /J _1 ≃0.44. For 0.5<J_2 /J_1 <0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s -wave character of the PVB order. For 0.44<J_2 /J_1 <0.5, spin order, dimer order, and spin gap are small on finite-size systems, which is consistent with a near-critical behavior. The critical exponents obtained from the finite-size spin and dimer correlations could be compatible with the deconfined criticality in this small region. We compare and contrast our results with earlier numerical studies.