Mutation of torsion pairs in triangulated categories and its geometric   realization
  We introduce and study mutation of torsion pairs, as a generalization of mutation of cluster tilting objects, rigid objects and maximal rigid objects. It is proved that any mutation of a torsion pair is again a torsion pair. A geometric realization of mutation of torsion pairs in the cluster category of type $A_n$ or $A_{\infty}$ is given via rotation of Ptolemy diagrams. 
Yu Zhou and Bin Zhu
math.RT math.CO math.RA