Geometric phase of a bipartite system with Dzyaloshinski-Moriya   interaction
  The Berry phase of a bipartite system described by a Heisenberg XXZ model driven by a one-site magnetic field is investigated. The effect of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the Berry phase is discussed. It is found that the DM interaction affects the Berry phase monotonously, and can also cause sudden change of the Berry phase for some weak magnetic field cases. 
Yue Zhou, Guo-Feng Zhang