  We have precisely determined the ground state phase diagram of the quantum
spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the
tensor renormalization group method. We find that the ferromagnetic,
ferroquadrupolar, and a large part of the antiferromagnetic phases are stable
against quantum fluctuations. However, around the phase where the ground state
is antiferroquadrupolar ordered in the classical limit, quantum fluctuations
suppress completely all magnetic orders, leading to a plaquette order phase
which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the
evidence of our numerical results, the quantum phase transition between the
antiferromagnetic phase and the plaquette phase is found to be either a direct
second order or a very weak first order transition.
