On the valence bond solid in the presence of Dzyaloshinskii-Moriya interaction

We examine the stability of the valence bond solid (VBS) phase against the Dzyaloshinskii-Moriya (DM) interaction in the bipartite lattice. We consider the VBS states in the AKLT model as well as the one in the Sandvik model in the 4×L lattice. We found that the VBS is very stable against the DM interaction qin the AKLT model. There is no quantum phase transition in the AKLT+DM case. However, the VBS spin gap closes in the Sandvik model due to the DM interaction.