Spontaneous dimerization in the spin-1 bilinear-biquadratic Heisenberg model on a honeycomb lattice

Within the linear flavor-wave theory, we show that due to the quantum order-by-disorder mechanism, the spin-1 bilinear-biquadratic Heisenberg model on a honeycomb lattice can spontaneously develop a columnar dimer order with a non-bipartite structure. The low-lying excitations above this novel ground state form several flat bands separated by nonzero energy gaps. Our results suggest that the quantum phase transition separating this dimerized phase with the nearby Néel-order phase may be of first order.