  Using infinite projected entangled pair states, we study the ground state
phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square
lattice directly in the thermodynamic limit. We find an unexpected partially
nematic partially magnetic phase in between the antiferroquadrupolar and
ferromagnetic regions. Furthermore, we describe all observed phases and discuss
the nature of the phase transitions involved.

Strongly Correlated Electrons