Infinite projected entangled pair states simulations of the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent Haldane phase in between the previously predicted antiferromagnetic and three-sublattice ${120}^{\circ }$ magnetically ordered phases. This intermediate phase preserves SU(2) spin and translational symmetry but breaks lattice rotational symmetry, and it can be adiabatically connected to the Haldane phase of decoupled $S=1$ chains. Our results contradict previous studies which found a direct transition between the two magnetically ordered states.

• Antiferromagnetism
• Frustrated magnetism
• Quantum spin liquid
• 2-dimensional systems
• Strongly correlated systems
• Heisenberg model
• Tensor network methods