Single Electron Spin Decoherence by Nuclear Spin Bath: Linked Cluster   Expansion Approach
  We develop a theoretical model for transverse dynamics of a single electron spin interacting with a nuclear spin bath. The approach allows a simple diagrammatic representation and analytical expressions of different nuclear spin excitation processes contributing to electron spin decoherence and dynamical phase fluctuations. It accounts for nuclear spin dynamics beyond conventional pair correlation models. As an illustration of the theory, we evaluated the coherence dynamics of a P donor electron spin in a Si crystal. 
S. K. Saikin, Wang Yao, L. J. Sham