# 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. (arXiv:1802.00874v1 [cond-mat.str-el])

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 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 N\'eel magnetic state to the stripe

magnetic state at $J_2/J_1 \simeq 0.549$, 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 a very small intermediate regime $\sim 0.005 J_1$

between the two magnetic order phases, which may imply the absent intermediate

phase. Both calculations identify that the stripe order comes with a

first-order transition at $J_2/J_1 \simeq 0.549$. Our results indicate that

unlike the spin-$1/2$ $J_1-J_2$ square model, quantum fluctuations in the

spin-$1$ model may be not strong enough to stabilize an intermediate

non-magnetic phase.