# 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.