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Making use of infinite projected entangled pair states, we investigate theground state phase diagram of the nearest-neighbor spin-1 bilinear-biquadraticHeisenberg model on the triangular lattice. In agreement with previous studies,we find the ferromagnetic, 120 degree magnetically ordered, ferroquadrupolarand antiferroquadrupolar phases, and confirm that all corresponding phasetransitions are first order. Moreover, we provide an accurate estimate of thelocation of the ferroquadrupolar to 120 degree magnetically ordered phasetransition, thereby fully establishing the phase diagram. Also, we do notencounter any signs of the existence of a quantum paramagnetic phase. Inparticular, contrary to the equivalent square lattice model, we demonstratethat on the triangular lattice the one-dimensional Haldane phase does not reachall the way up to the two-dimensional limit. Finally, we investigate thepossibility of an intermediate partially-magnetic partially-quadrupolar phaseclose to $\theta = \pi/2$, and we show that, also contrary to the squarelattice case, this phase is not present on the triangular lattice.

A ground state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks