Spin and orbital valence bond solids in a one-dimensional spin-orbital   system: Schwinger boson mean field theory
  A generalized one-dimensional $SU(2)\times SU(2)$ spin-orbital model is studied by Schwinger boson mean-field theory (SBMFT). We explore mainly the dimer phases and clarify how to capture properly the low temperature properties of such a system by SBMFT. The phase diagrams are exemplified. The three dimer phases, orbital valence bond solid (OVB) state, spin valence bond solid (SVB) state and spin-orbital valence bond solid (SOVB) state, are found to be favored in respectively proper parameter regions, and they can be characterized by the static spin and pseudospin susceptibilities calculated in SBMFT scheme. The result reveals that the spin-orbit coupling of $SU(2)\times SU(2)$ type serves as both the spin-Peierls and orbital-Peierles mechanisms that responsible for the spin-singlet and orbital-singlet formations respectively. 
Peng Li and Shun-Qing Shen