Spin-Orbital Entanglement and Phase Diagram of Spin-orbital Chain with   $SU(2) \times SU(2)$ Symmetry
  Spin-orbital entanglement in quantum spin-orbital systems is quantified by a reduced von Neumann entropy, and is calculated for the ground state of a coupled spin-orbital chain with $SU(2)\times SU(2)$ symmetry. By analyzing the discontinuity and local extreme of the reduced entropy as functions of the model parameters, we deduce a rich phase diagram to describe the quantum phase transitions in the model. Our approach provides an efficient and powerful method to identify phase boundaries in a system with complex correlation between multiply degrees of freedom. 
Yan Chen, Z. D. Wang, Y. Q. Li, and F. C. Zhang