Spontaneous dimerization in the spin-1 bilinear-biquadratic Heisenberg   model on a honeycomb lattice
  Within the linear flavor-wave theory, we show that, caused by quantum order-by-disorder mechanism, the spin-1 bilinear-biquadratic Heisenberg model defined 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 N\'{e}el-order one may be of first order. 
Yu-Wen Lee and Min-Fong Yang
cond-mat.str-el