Quantum phase diagram of spin-1 J_1-J_2 Heisenberg model on the square lattice: An infinite projected entangled-pair state and density matrix renormalization group study

摘要

We study the spin-1 Heisenberg model on the square lattice with the antiferromagnetic nearest-neighbor J_1 and the next-nearest-neighbor J_2 couplings by using the infinite projected entangled-pair state (iPEPS) ansatz and the density matrix renormalization group (DMRG) calculation. The iPEPS simulation, which studies the model directly in the thermodynamic limit, finds a crossing of the ground state from the Neel magnetic state to the stripe magnetic state at J_2/_1 ≈ 0.549, showing a direct phase transition. In the finite-size DMRG calculation on the cylinder geometry up to the cylinder width L_y = 10, we find that around the same critical point the Neel and the stripe orders are strongly suppressed, which implies the absence of an intermediate phase. Both calculations identify that the stripe order comes with a first-order transition at J_2/J_1 ≈ 0.549. Our results indicate that unlike the spin-1 /2 J_1-J_2 square model, quantum fluctuations in the spin-1 model may not be strong enough to stabilize an intermediate nonmagnetic phase.